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   "source": [
    "# Numerical Solvers for Delay Differential Equations\n",
    "\n",
    "[![Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/brainpy/brainpy/blob/master/docs_version2/tutorial_toolbox/dde_numerical_solvers.ipynb)\n",
    "[![Open in Kaggle](https://kaggle.com/static/images/open-in-kaggle.svg)](https://kaggle.com/kernels/welcome?src=https://github.com/brainpy/brainpy/blob/master/docs_version2/tutorial_toolbox/dde_numerical_solvers.ipynb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "@[Chaoming Wang](https://github.com/chaoming0625)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "In real world systems, **delay** is very often encountered in many practical systems, such as automatic control, biology, economics and long transmission lines. The **delayed differential equation (DDEs)** is used to describe these dynamical systems.\n",
    "\n",
    "Delay differential equations (DDEs) are a type of differential equation in which the derivative at a certain time is given in terms of the values of the function at previous times.\n",
    "\n",
    "Let's take delay ODEs as the example. The simplest **constant delay** equations have the form\n",
    "\n",
    "$$\n",
    "y'(t) = f(t, y(t), y(t-\\tau_1), y(t-\\tau_2),\\ldots, y(t-\\tau_k))\n",
    "$$\n",
    "\n",
    "where the time delays (lags) $\\tau_j$ are positive constants.\n",
    "\n",
    "For **neutral type DDE** delays appear in derivative terms,\n",
    "\n",
    "$$\n",
    "y'(t) = f(t, y(t), y'(t-\\tau_1), y'(t-\\tau_2),\\ldots, y'(t-\\tau_k))\n",
    "$$\n",
    "\n",
    "More generally, **state dependent** delays may depend on the solution, that is $\\tau_i = \\tau_i (t,y(t))$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   },
   "source": [
    "In BrainPy, we support delay differential equations based on delay variables. Specifically, for state-dependent delays, we have:\n",
    "\n",
    "- [brainpy.math.TimeDelay](../apis/auto/math/generated/brainpy.math.delay_vars.TimeDelay.rst)\n",
    "- [brainpy.math.LengthDelay](../apis/auto/math/generated/brainpy.math.delay_vars.LengthDelay.rst)\n",
    "\n",
    "For neutral-type delays, we use:\n",
    "\n",
    "- [brainpy.math.NeuTimeDelay](../apis/auto/math/generated/brainpy.math.delay_vars.NeuTimeDelay.rst)\n",
    "- [brainpy.math.NeuLenDelay](../apis/auto/math/generated/brainpy.math.delay_vars.NeuLenDelay.rst)"
   ]
  },
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     "start_time": "2025-10-06T04:05:19.681761Z"
    }
   },
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import brainpy as bp\n",
    "import brainpy.math as bm\n",
    "\n",
    "bm.enable_x64()\n",
    "\n",
    "bp.__version__"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'3.0.0'"
      ]
     },
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    }
   ],
   "execution_count": 1
  },
  {
   "cell_type": "markdown",
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   },
   "source": [
    "## Delay variables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "For an ODE system, the numerical methods need to know its initial condition $y(t_0)=y_0$ and its derivative rule $y'(t_0) = y'_0$. However, for DDEs, it is not enough to give a set of initial values for the function and its derivatives at $t_0$, but one must give a set of functions to provide the historical values for  $t_0 - max(\\tau) \\leq t \\leq t_0$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Therefore, you need some delay variables to wrap the variable delays. ``brainpy.math.TimeDelay`` can be used to define delay variables which depend on states, and ``brainpy.math.NeuTimeDelay`` is used to define delay variables which depend on the derivative."
   ]
  },
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   "cell_type": "code",
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     "end_time": "2025-10-06T04:05:23.876366Z",
     "start_time": "2025-10-06T04:05:23.680940Z"
    }
   },
   "source": [
    "d = bm.TimeDelay(bm.zeros(2), delay_len=10, dt=1, t0=0, before_t0=lambda t: t)"
   ],
   "outputs": [],
   "execution_count": 2
  },
  {
   "cell_type": "code",
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2025-10-06T04:05:24.112507Z",
     "start_time": "2025-10-06T04:05:23.883400Z"
    }
   },
   "source": [
    "d(0.)"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array([0., 0.], dtype=float64)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 3
  },
  {
   "cell_type": "code",
   "metadata": {
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    "ExecuteTime": {
     "end_time": "2025-10-06T04:05:24.225237Z",
     "start_time": "2025-10-06T04:05:24.117108Z"
    }
   },
   "source": [
    "d(-0.5)"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array([-0.5, -0.5], dtype=float64)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 4
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Request a time beyond $(max\\_delay, t_0)$ will cause an error."
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2025-10-06T04:05:24.351870Z",
     "start_time": "2025-10-06T04:05:24.229843Z"
    }
   },
   "source": [
    "try:\n",
    "    d(0.1)\n",
    "except Exception as e:\n",
    "    print(e)"
   ],
   "outputs": [],
   "execution_count": 5
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "## Delay ODEs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Here we illustrate how to make numerical integration of delay ODEs with several examples. Before that, we define a general function to simulate a delay ODE function."
   ]
  },
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   "cell_type": "code",
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    }
   },
   "source": [
    "def delay_odeint(duration, eq, args=None, inits=None,\n",
    "                 state_delays=None, neutral_delays=None,\n",
    "                 monitors=('x',), method='euler', dt=0.1):\n",
    "    # define integrators of ODEs based on `brainpy.odeint`\n",
    "    dde = bp.odeint(eq,\n",
    "                    state_delays=state_delays,\n",
    "                    neutral_delays=neutral_delays,\n",
    "                    method=method)\n",
    "    # define IntegratorRunner\n",
    "    runner = bp.IntegratorRunner(dde,\n",
    "                                 monitors=monitors,\n",
    "                                 dt=dt,\n",
    "                                 inits=inits)\n",
    "    runner.run(duration, args=args)\n",
    "    return runner.mon"
   ],
   "outputs": [],
   "execution_count": 6
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "#### Example #1: First-order DDE with one constant delay and a constant initial history function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Let the following DDE be given:\n",
    "\n",
    "$$\n",
    "y'(t)=-y(t-1)\n",
    "$$\n",
    "\n",
    "where the delay is 1 s. the example compares the solutions of three different cases using three different constant history functions:\n",
    "\n",
    "- Case #1: $\\phi(t)=-1$\n",
    "- Case #2: $\\phi(t)=0$\n",
    "- Cas3 #3: $\\phi(t)=1$"
   ]
  },
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    }
   },
   "source": [
    "def equation(x, t, xdelay):\n",
    "    return -xdelay(t - 1)\n",
    "\n",
    "\n",
    "case1_delay = bm.TimeDelay(bm.zeros((1,)), 1., before_t0=-1., interp_method='round')\n",
    "case2_delay = bm.TimeDelay(bm.zeros((1,)), 1., before_t0=0., interp_method='round')\n",
    "case3_delay = bm.TimeDelay(bm.zeros((1,)), 1., before_t0=1., interp_method='round')"
   ],
   "outputs": [],
   "execution_count": 7
  },
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     "end_time": "2025-10-06T04:05:25.267166Z",
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    }
   },
   "source": [
    "case1 = delay_odeint(20., equation, args={'xdelay': case1_delay},\n",
    "                     state_delays={'x': case1_delay})  # delay for variable \"x\"\n",
    "case2 = delay_odeint(20., equation, args={'xdelay': case2_delay}, state_delays={'x': case2_delay})\n",
    "case3 = delay_odeint(20., equation, args={'xdelay': case3_delay}, state_delays={'x': case3_delay})"
   ],
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   },
   "source": [
    "fig, axs = plt.subplots(3, 1)\n",
    "fig.tight_layout(rect=[0, 0, 1, 0.95], pad=3.0)\n",
    "fig.suptitle(\"$y'(t)=-y(t-1)$\")\n",
    "\n",
    "axs[0].plot(case1.ts, case1.x, color='red', linewidth=1)\n",
    "axs[0].set_title('$\\phi(t)=-1$')\n",
    "\n",
    "axs[1].plot(case2.ts, case2.x, color='red', linewidth=1)\n",
    "axs[1].set_title('$\\phi(t)=0$')\n",
    "\n",
    "axs[2].plot(case3.ts, case3.x, color='red', linewidth=1)\n",
    "axs[2].set_title('$\\phi(t)=1$')\n",
    "\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<>:6: SyntaxWarning: invalid escape sequence '\\p'\n",
      "<>:9: SyntaxWarning: invalid escape sequence '\\p'\n",
      "<>:12: SyntaxWarning: invalid escape sequence '\\p'\n",
      "<>:6: SyntaxWarning: invalid escape sequence '\\p'\n",
      "<>:9: SyntaxWarning: invalid escape sequence '\\p'\n",
      "<>:12: SyntaxWarning: invalid escape sequence '\\p'\n",
      "C:\\Users\\adadu\\AppData\\Local\\Temp\\ipykernel_57168\\1503675638.py:6: SyntaxWarning: invalid escape sequence '\\p'\n",
      "  axs[0].set_title('$\\phi(t)=-1$')\n",
      "C:\\Users\\adadu\\AppData\\Local\\Temp\\ipykernel_57168\\1503675638.py:9: SyntaxWarning: invalid escape sequence '\\p'\n",
      "  axs[1].set_title('$\\phi(t)=0$')\n",
      "C:\\Users\\adadu\\AppData\\Local\\Temp\\ipykernel_57168\\1503675638.py:12: SyntaxWarning: invalid escape sequence '\\p'\n",
      "  axs[2].set_title('$\\phi(t)=1$')\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 3 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 9
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example #2: First-order DDE with one constant delay and a non constant initial history function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let the following DDE be given:\n",
    "\n",
    "$$\n",
    "y'(t)=-y(t-2)\n",
    "$$\n",
    "\n",
    "where the delay is 2 s; the example compares the solutions of four different cases using two different non constant history functions and two different intervals of $t$:\n",
    "\n",
    "- Case #1: $\\phi(t)=e^{-t} - 1, t \\in [0, 4]$\n",
    "- Case #2: $\\phi(t)=e^{t} - 1, t \\in [0, 4]$\n",
    "- Case #3: $\\phi(t)=e^{-t} - 1, t \\in [0, 60]$\n",
    "- Case #4: $\\phi(t)=e^{t} - 1, t \\in [0, 60]$"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-06T04:05:25.749622Z",
     "start_time": "2025-10-06T04:05:25.662113Z"
    }
   },
   "source": [
    "def make_eq(xdelay):\n",
    "    def eq(x, t): return -xdelay(t - 2)\n",
    "\n",
    "    return eq\n",
    "\n",
    "\n",
    "delay1 = bm.TimeDelay(bm.zeros(1), 2., before_t0=lambda t: bm.exp(-t) - 1, dt=0.01, interp_method='round')\n",
    "delay2 = bm.TimeDelay(bm.zeros(1), 2., before_t0=lambda t: bm.exp(t) - 1, dt=0.01, interp_method='round')\n",
    "delay3 = bm.TimeDelay(bm.zeros(1), 2., before_t0=lambda t: bm.exp(-t) - 1, dt=0.01, interp_method='round')\n",
    "delay4 = bm.TimeDelay(bm.zeros(1), 2., before_t0=lambda t: bm.exp(t) - 1, dt=0.01, interp_method='round')"
   ],
   "outputs": [],
   "execution_count": 10
  },
  {
   "cell_type": "code",
   "metadata": {
    "scrolled": false,
    "ExecuteTime": {
     "end_time": "2025-10-06T04:05:26.522746Z",
     "start_time": "2025-10-06T04:05:25.754754Z"
    }
   },
   "source": [
    "case1 = delay_odeint(4., make_eq(delay1), state_delays={'x': delay1}, dt=0.01)\n",
    "case2 = delay_odeint(4., make_eq(delay2), state_delays={'x': delay2}, dt=0.01)\n",
    "case3 = delay_odeint(60., make_eq(delay3), state_delays={'x': delay3}, dt=0.01)\n",
    "case4 = delay_odeint(60., make_eq(delay4), state_delays={'x': delay4}, dt=0.01)"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "  0%|          | 0/400 [00:00<?, ?it/s]"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "2e03e7816d6d46758ca070d9f1b5a8d4"
      }
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "  0%|          | 0/400 [00:00<?, ?it/s]"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "b5b0f16613f146a6907d719c5697fc4d"
      }
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "  0%|          | 0/6000 [00:00<?, ?it/s]"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "6058dc9c10a943158e99da1b80e2f4f6"
      }
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "  0%|          | 0/6000 [00:00<?, ?it/s]"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "20127f3c0ec2490aa2e339ce51483a27"
      }
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 11
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-06T04:05:26.839071Z",
     "start_time": "2025-10-06T04:05:26.536499Z"
    }
   },
   "source": [
    "fig, axs = plt.subplots(2, 2)\n",
    "fig.tight_layout(rect=[0, 0, 1, 0.95], pad=3.0)\n",
    "fig.suptitle(\"$y'(t)=-y(t-2)$\")\n",
    "\n",
    "axs[0, 0].plot(case1.ts, case1.x, color='red', linewidth=1)\n",
    "axs[0, 0].set_title('$\\phi(t)=e^{-t} - 1, t \\in [0, 4]$')\n",
    "\n",
    "axs[0, 1].plot(case2.ts, case2.x, color='red', linewidth=1)\n",
    "axs[0, 1].set_title('$\\phi(t)=e^t - 1, t \\in [0, 4]$')\n",
    "\n",
    "axs[1, 0].plot(case3.ts, case3.x, color='red', linewidth=1)\n",
    "axs[1, 0].set_title('$\\phi(t)=e^{-t} - 1, t \\in [0, 60]$')\n",
    "\n",
    "axs[1, 1].plot(case4.ts, case4.x, color='red', linewidth=1)\n",
    "axs[1, 1].set_title('$\\phi(t)=e^t - 1, t \\in [0, 60]$')\n",
    "\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<>:6: SyntaxWarning: invalid escape sequence '\\p'\n",
      "<>:9: SyntaxWarning: invalid escape sequence '\\p'\n",
      "<>:12: SyntaxWarning: invalid escape sequence '\\p'\n",
      "<>:15: SyntaxWarning: invalid escape sequence '\\p'\n",
      "<>:6: SyntaxWarning: invalid escape sequence '\\p'\n",
      "<>:9: SyntaxWarning: invalid escape sequence '\\p'\n",
      "<>:12: SyntaxWarning: invalid escape sequence '\\p'\n",
      "<>:15: SyntaxWarning: invalid escape sequence '\\p'\n",
      "C:\\Users\\adadu\\AppData\\Local\\Temp\\ipykernel_57168\\3939652715.py:6: SyntaxWarning: invalid escape sequence '\\p'\n",
      "  axs[0, 0].set_title('$\\phi(t)=e^{-t} - 1, t \\in [0, 4]$')\n",
      "C:\\Users\\adadu\\AppData\\Local\\Temp\\ipykernel_57168\\3939652715.py:9: SyntaxWarning: invalid escape sequence '\\p'\n",
      "  axs[0, 1].set_title('$\\phi(t)=e^t - 1, t \\in [0, 4]$')\n",
      "C:\\Users\\adadu\\AppData\\Local\\Temp\\ipykernel_57168\\3939652715.py:12: SyntaxWarning: invalid escape sequence '\\p'\n",
      "  axs[1, 0].set_title('$\\phi(t)=e^{-t} - 1, t \\in [0, 60]$')\n",
      "C:\\Users\\adadu\\AppData\\Local\\Temp\\ipykernel_57168\\3939652715.py:15: SyntaxWarning: invalid escape sequence '\\p'\n",
      "  axs[1, 1].set_title('$\\phi(t)=e^t - 1, t \\in [0, 60]$')\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 4 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 12
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example #3: First-order DDE with two constant delays and a constant initial history function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let the following DDE be given:\n",
    "\n",
    "$$\n",
    "y'(t)=-y(t - 1) + 0.3 y(t - 2)\n",
    "$$\n",
    "\n",
    "where the delays are two and are both constants equal to 1s and 2s respectively; The initial historical function is also constant and is $\\phi(t)=1$."
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-06T04:05:27.094988Z",
     "start_time": "2025-10-06T04:05:26.843371Z"
    }
   },
   "source": [
    "def eq(x, t):\n",
    "    return -delay(t - 1) + 0.3 * delay(t - 2)\n",
    "\n",
    "\n",
    "delay = bm.TimeDelay(bm.ones(1), 2., before_t0=1., dt=0.01, interp_method='round')\n",
    "mon = delay_odeint(10., eq, inits=[1.], state_delays={'x': delay}, dt=0.01)"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "  0%|          | 0/1000 [00:00<?, ?it/s]"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "f05f01e014ba476aa5191e45de1beb20"
      }
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 13
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-06T04:05:27.208155Z",
     "start_time": "2025-10-06T04:05:27.101564Z"
    }
   },
   "source": [
    "fig, axs = plt.subplots(1, 1)\n",
    "fig.tight_layout(rect=[0, 0, 1, 0.95], pad=3.0)\n",
    "fig.suptitle(\"$y'(t)=-y(t-1) + 0.3\\ y(t-2)$\")\n",
    "\n",
    "axs.plot(mon.ts, mon.x, color='red', linewidth=1)\n",
    "axs.set_title('$\\phi(t)=1$')\n",
    "\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<>:3: SyntaxWarning: invalid escape sequence '\\ '\n",
      "<>:6: SyntaxWarning: invalid escape sequence '\\p'\n",
      "<>:3: SyntaxWarning: invalid escape sequence '\\ '\n",
      "<>:6: SyntaxWarning: invalid escape sequence '\\p'\n",
      "C:\\Users\\adadu\\AppData\\Local\\Temp\\ipykernel_57168\\3402231415.py:3: SyntaxWarning: invalid escape sequence '\\ '\n",
      "  fig.suptitle(\"$y'(t)=-y(t-1) + 0.3\\ y(t-2)$\")\n",
      "C:\\Users\\adadu\\AppData\\Local\\Temp\\ipykernel_57168\\3402231415.py:6: SyntaxWarning: invalid escape sequence '\\p'\n",
      "  axs.set_title('$\\phi(t)=1$')\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 14
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example #4: System of two first-order DDEs with one constant delay and two constant initial history functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let the following system of DDEs be given:\n",
    "\n",
    "$$\n",
    "\\begin{cases}\n",
    "    y_1'(t) = y_1(t) y_2(t-0.5)\n",
    "    \\\\\n",
    "    y_2'(t) = y_2(t) y_1(t-0.5)\n",
    "\\end{cases}\n",
    "$$\n",
    "\n",
    "where the delay is only one, constant and equal to 0.5 s and the initial historical functions are also constant; for what we said at the beginning of the post these must be two, in fact being the order of the system of first degree you need one for each unknown and they are: $y_1(t)=1, y_2(t)=-1$. "
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "lines_to_next_cell": 2,
    "ExecuteTime": {
     "end_time": "2025-10-06T04:05:27.596478Z",
     "start_time": "2025-10-06T04:05:27.227136Z"
    }
   },
   "source": [
    "def eq(x, y, t):\n",
    "    dx = x * ydelay(t - 0.5)\n",
    "    dy = y * xdelay(t - 0.5)\n",
    "    return dx, dy\n",
    "\n",
    "\n",
    "xdelay = bm.TimeDelay(bm.ones(1), 0.5, before_t0=1., dt=0.01, interp_method='round')\n",
    "ydelay = bm.TimeDelay(-bm.ones(1), 0.5, before_t0=-1., dt=0.01, interp_method='round')\n",
    "\n",
    "mon = delay_odeint(3., eq, inits=[1., -1], state_delays={'x': xdelay, 'y': ydelay},\n",
    "                   dt=0.01, monitors=['x', 'y'])"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "  0%|          | 0/300 [00:00<?, ?it/s]"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "191da1ac4c81435095287c8b1649ae95"
      }
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 15
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-06T04:05:27.726577Z",
     "start_time": "2025-10-06T04:05:27.611180Z"
    }
   },
   "source": [
    "fig, axs = plt.subplots(1, 1)\n",
    "fig.tight_layout(rect=[0, 0, 1, 0.95], pad=3.0)\n",
    "fig.suptitle(\"$x'(t)=x(t) y(t-d); y'(t)=y(t) x(t-d)$\")\n",
    "\n",
    "axs.plot(mon.ts, mon.x.flatten(), color='red', linewidth=1)\n",
    "axs.plot(mon.ts, mon.y.flatten(), color='blue', linewidth=1)\n",
    "axs.set_title('$\\phi_x(t)=1; \\phi_y(t)=-1; d=0.5$')\n",
    "\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<>:7: SyntaxWarning: invalid escape sequence '\\p'\n",
      "<>:7: SyntaxWarning: invalid escape sequence '\\p'\n",
      "C:\\Users\\adadu\\AppData\\Local\\Temp\\ipykernel_57168\\1815711682.py:7: SyntaxWarning: invalid escape sequence '\\p'\n",
      "  axs.set_title('$\\phi_x(t)=1; \\phi_y(t)=-1; d=0.5$')\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 16
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example #5: Second-order DDE with one constant delay and two constant initial history functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let the following DDE be given:\n",
    "\n",
    "$$\n",
    "y(t)'' = -y'(t) - 2y(t) - 0.5 y(t-1)\n",
    "$$\n",
    "\n",
    "where the delay is only one, constant and equal to 1 s. Since the DDE is second order, in that the second derivative of the unknown function appears, the historical functions must be two, one to give the values of the unknown $y(t)$ for $t <= 0$,  and one and one to provide the value of the first derivative $y'(t)$ also for $t <= 0$. \n",
    "\n",
    "In this example they are the following two constant functions: $y(t)=1, y'(t)=0$.\n",
    "\n",
    "Due to the properties of the second-order equations, the given DDE is equivalent to the following system of first-order equations:\n",
    "\n",
    "$$\n",
    "\\begin{cases}\n",
    "    y_1'(t) = y_2(t)\n",
    "    \\\\\n",
    "    y_2'(t) = -y_1'(t) - 2y_1(t) - 0.5 y_1(t-1)\n",
    "\\end{cases}\n",
    "$$\n",
    "\n",
    "and so the implementation falls into the case of the previous example of systems of first-order equations."
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-06T04:05:28.053841Z",
     "start_time": "2025-10-06T04:05:27.756778Z"
    }
   },
   "source": [
    "def eq(x, y, t):\n",
    "    dx = y\n",
    "    dy = -y - 2 * x - 0.5 * xdelay(t - 1)\n",
    "    return dx, dy\n",
    "\n",
    "\n",
    "xdelay = bm.TimeDelay(bm.ones(1), 1., before_t0=1., dt=0.01, interp_method='round')\n",
    "mon = delay_odeint(16., eq, inits=[1., 0.], state_delays={'x': xdelay}, monitors=['x', 'y'], dt=0.01)"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "  0%|          | 0/1600 [00:00<?, ?it/s]"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "8fee3e886cfa40c3a90efb17749f68ab"
      }
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 17
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-06T04:05:28.202070Z",
     "start_time": "2025-10-06T04:05:28.077081Z"
    }
   },
   "source": [
    "fig, axs = plt.subplots(1, 1)\n",
    "fig.tight_layout(rect=[0, 0, 1, 0.95], pad=3.0)\n",
    "fig.suptitle(\"$y''(t)=-y'(t) - 2 y(t) - 0.5 y(t-1)$\")\n",
    "axs.plot(mon.ts, mon.x[:, 0], color='red', linewidth=1)\n",
    "axs.plot(mon.ts, mon.y[:, 0], color='green', linewidth=1)\n",
    "axs.set_title('$ih \\, f_y(t)=1; \\phi\\,dy/dt(t)=0$')\n",
    "\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<>:6: SyntaxWarning: invalid escape sequence '\\,'\n",
      "<>:6: SyntaxWarning: invalid escape sequence '\\,'\n",
      "C:\\Users\\adadu\\AppData\\Local\\Temp\\ipykernel_57168\\3497153139.py:6: SyntaxWarning: invalid escape sequence '\\,'\n",
      "  axs.set_title('$ih \\, f_y(t)=1; \\phi\\,dy/dt(t)=0$')\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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iTWASRKQFffr0QadOnQp/Dg0NRdOmTREUFIQBAwbA0tIS9erVw3fffVfs8a+88gpMTU2Rn5+PWbNmQaVSoUOHDmWWGxUVhZCQEPTu3bvI9rZt22LMmDEAAE9PT6hUKtjY2BQ+HxAQADs7O+zYsaMSV1s+xsbGcHJyKvf+kZGRiI6OLnO/bdu2FekL1KVLF4wZMwbJycmlHrdp0ya0aNECJiYmCAgIwLlz5xAWFgYvLy8YGRlh4MCBaNCgwVPHCSHQqlUrdOnSpcj2PXv2YNCgQRUup7TXRsmvJwD89ddf0NfXx6RJkwq3mZiY4JVXXsHp06dx9+5drZZPVFUGcgdAVBOFhITgueeeK/w5NDQUjo6OGDx4MF5++WUMGzYMv/zyC6ZOnYqePXs+1QdlzJgxMDQ0xPLly/Hdd9/Bzs4O7u7uZZZ76tQpAE/XDsyYMQNz585FdnY2Zs+eDQBFPjQLjjl58mSx583NzS0zqShgZ2dXpO9KZTVt2hTdunXDkSNHStxn0aJFmD59Ol588UXk5uYiJSUF/fv3x/LlyyGEwIYNG4o9bsmSJZg2bRqGDRuGN954AyEhIRg8eDBsbGwK712bNm2wd+9eJCYmwtbWtvDYjRs34tKlSzhx4kThtpiYGFy6dAnz5s2rcDmlvTZKfz0vXboELy8vWFlZFdnetm1bAEBwcHCFaj+JdE7u9jiimiY2NlYAED/99JMQQogHDx4IAMLe3r5In6Dw8HABQKxZs6bY83z00UfC3Nxc5Ofnl7vsWbNmCQAiNTX1qefc3NzESy+9VOKxkyZNEqampsU+FxgYKACU6xEVFVVmnOfPny+zTxAA0a1btxKfP3funFCpVOL9998XQgjh5eUlXnzxRSGEEH369BEGBgYiPT39qeMuXbokDAwMxEcffVRk++TJkwUAMX/+fCGEEDt37hQAxKFDhwr3ycnJEY0aNRJDhgwpcuzKlSuFqampyMjIqHA5QpT82ij99fT19RU9e/Z8antYWJgAIJYtW1bisURKwJogIg0LCQkBgMLanYKf582bV+S/YkNDQwCAkZFRiefx9fWtUK3Ko0ePYGBgAAsLiyLbk5OTER0dXTharTi2trbIzMxERkYGzMzMijzn7+9f7hE/FWnyKo0QotTnv/rqKzg4OGDevHnIzMzEjRs3MHHiRABAp06dcODAAcTFxT3VpPX555/D2toaH3/8cZHt3bp1w88//1z4urVp0wYAEBQUhJ49ewIAVqxYgaioKGzfvr3IsX///Td69OgBU1PTCpdT2muj9NczMzMTxsbGT20v6L+UmZlZrjKI5MIkiEjDQkNDAfybBBX8/N/5ayIjIwEATZo0KfY8ly9fRr9+/TQSU0EiVtqHZkHSUdCZ+0m2trZP9UuRU15eHvbt24fhw4fD1NQU58+fh1qtLry+9PR0ACjSjAVIw7n//vtvTJo06anEIC8vD8C/r5uTkxPq1auHS5cuFZ5z/vz5GDt2LJo1a1Z4XG5uLg4cOIAFCxZUqpzyvDb/pZTX09TUtNj5iLKysgqfJ1IyJkFEGhYSEgI3NzdYW1sDkJKgevXqPfUf9eXLl2FgYFDsaKakpCTcvXu3wvPV1KlTB3l5eUhNTYWlpWWRmACpBqAkiYmJMDMzK/aDKycnB48fPy5XDA4ODtDX169Q3BV148aNIvPs/Pf6goOD4e7uXvgaFLh58yYyMjIQEBDw1DkvXLgACwsLeHh4FG5r06ZNYRL0zTffIDEx8al+PydOnEBKSgoGDhxYqXJKe22U/no6Ozvj/v37T21/+PAhAMDFxaVcZRDJhaPDiDQsJCSkyH/ooaGhxf7HHhISAi8vr2KbE4r7T//x48cwMDBARkZG4bZNmzahW7duhT97e3sDkEYV/fd8zs7OsLe3LzHuqKioEoeGnzp1Cs7OzuV66GJEUGJiIgDA3NwcgJRQ2tvbw8XFBQkJCTh69CiGDh361HFP3rsnpaenY+3atfD19S1Sc9KmTRtcvXoV0dHRWLx4MSZPnvxUB/U9e/bAx8enSLNbRcop7bVR+uvZokULXLt2DSkpKUW2nz17tvB5IiVjTRCRBuXn5yM8PBz9+/cv/DkiIqLYZq3Lly+jZcuWxZ7n8uXLAIomQXZ2dnB1dUVISAjat2+PvLw8zJ49G7/99lvhPgXD6C9cuFDk2OjoaNSvX7/U2IOCggqHXf+XHH2CSlOvXj0AwOnTp/H6668jJCSksFZk6tSp0NPTw7vvvvvUcQUJzOHDhzF27NjC7Z999hkeP378VM1b69atoVarMXr0aAghnurfA0j9gQYPHlzpckp7bZT+eg4fPhyLFy/GihUr8P777wOQmgJXrVqFdu3acWQYKR6TICINun79OrKysgo/5Ap+/m9NUEFH3gkTJhR7npCQENSrVw92dnZFtrdu3RqXLl1C+/btsXr1ajRq1KjIfEQNGzZEs2bNcPDgwcJOwgDg4eGBw4cPY+HChXBxcUHTpk2LNNVcvHgRjx8/Lrb2BNBcH5KlS5ciKSkJDx48AADs2rUL9+7dAwC89dZbRZqvVCpViUPk3dzc0L17d6xbtw6Ojo64fPkymjVrhiFDhmDv3r1Ys2ZNkWatAg4ODujbty9Wr14NY2NjtGzZEvv27Ssc7l5cEgQAJ0+exNy5c+Hg4FDk+aioKERERODnn3+udDmlvTZKfz3btWuHF154ATNnzkRcXBwaN26MNWvW4Pbt21i5cmWVz0+kdfIOTiOqWTZv3iwAiLCwsCI//3cphXPnzgkAYvfu3cWep23btmLAgAFPbf/yyy/Fa6+9JrKysoSbm5u4ePHiU/t88803wsLCoshw7fv374t+/foJCwsLAUB8//33RY6ZMWOGcHNz0/oyC+7u7uUaip2amioAiFGjRpV4rocPH4rBgwcLExMTAUAYGRmJTp06FRnSXtJxzzzzjLC0tBR16tQRI0eOFOvXr39qOHyBBg0aCAcHh2KHqS9dulRYW1uL3NzcSpdT1muj5NdTCCEyMzPF+++/L5ycnISxsbFo06aN2Ldvn9bLJdIEJkFE1cjBgwdF69atxZIlS8Tzzz9f7D5JSUnCzs5O/Prrr+U6Z1ZWlnBychLffvutJkOtkj179giVSiVCQkLK3LdgHa5Lly5pPI6bN28KfX198d133xX7/IABA8QLL7yg8XKfVBNeTyKlYsdoomokICAAYWFh+Oqrr54apVTA2toa06dPx6JFi6BWq8s856pVq2BoaIjXX39d0+FWWmBgIEaNGlWu0XGRkZFQqVQlTjVQFTNnzkSDBg1KvDfdu3fH1KlTNV7uk2rC60mkVCohypiRjIgUpXHjxujYsSPWrl0rdyiK8Oqrr+LgwYO4ffu2Rs6XlJSEvXv34siRI/jll1+wd+9ejc3XRETKwo7RRNVIWloa0tPTMXfuXLlDUYzIyMjCoeSacOjQIYwePRr169fH8uXLmQAR1WCsCSKqRqZOnYr8/Hx8//33codCRFTtsU8QUTUQHBwMa2trhISE4IsvvpA7HCKiGoE1QURERFQrsSaIiIiIaqUa1zFarVbjwYMHsLS0LHb1ZCIiIqq5hBBITU2Fi4sL9PRKr+upcUnQgwcPuF4NERFRLXf37t0y19ircUmQpaUlAOniraysZI6GiIiIdCklJQWurq6F+UBpalwSVNAEZmVlxSSIiIiolipPlxh2jCYiIqJaiUkQERER1UpMgoiIiKhWYhJEREREtRKTICIiIqqVmAQRERFRrcQkiIiIiGolJkFERERUKzEJIiIiolpJq0nQsWPHMGTIELi4uEClUmH79u1lHnPkyBG0atUKxsbGaNy4MVavXq3NEImIiKiW0moSlJ6eDn9/f/z444/l2j8qKgqDBg1Cjx49EBwcjHfffRevvvoq9u/fr80wiYiIqBbS6tphAwYMwIABA8q9/7Jly+Dh4YGvv/4aANC0aVOcOHECS5YsQb9+/Yo9Jjs7G9nZ2YU/p6SkVC3oshw6BPj5AQ4O2i2HiIiItEpRfYJOnz6N3r17F9nWr18/nD59usRjFixYAGtr68KHq6ur9gLMyAD69wccHYHJk4GsLO2VRURERFqlqCQoJiYGjo6ORbY5OjoiJSUFmZmZxR4zc+ZMJCcnFz7u3r2rvQDNzICoKGDxYmDNGuCZZ4CcHO2VR0RERFqjqCSoMoyNjWFlZVXkoVX16wPTpgF79gBHjgAffqjd8oiIiEgrFJUEOTk5ITY2tsi22NhYWFlZwdTUVKaoStCjB/Dll8C33wLnz8sdDREREVWQopKgDh064NChQ0W2HThwAB06dJApojK8/bbUSXrKFECtljsaIiIiqgCtJkFpaWkIDg5GcHAwAGkIfHBwMKKjowFI/XnGjx9fuP/rr7+OW7duYfr06YiMjMRPP/2EzZs3Y+rUqdoMs/IMDIDvvgPOnQN27ZI7GiIiIqoArSZBFy5cQMuWLdGyZUsAwLRp09CyZUvMnj0bAPDw4cPChAgAPDw8sGfPHhw4cAD+/v74+uuv8euvv5Y4PF4RunUDunQBvvgCEELuaIiIiKicVELUrE/ulJQUWFtbIzk5WfudpAvs3QsMHAgcPQp07aqbMomIiOgpFckDFNUnqNrq3x9o3Bj45Re5IyEiIqJyYhKkCSoV8OqrwF9/AYmJckdDRERE5cAkSFMmTADy8oD16+WOhIiIiMqBSZCmODkBgwdLM0kTERGR4jEJ0qRRo4ALF6SlNYiIiEjRmARp0qBBgImJ1DeIiIiIFI1JkCZZWEhD5TdvljsSIiIiKgOTIE0bMUJqErt9W+5IiIiIqBRMgjRtwABpOY2//5Y7EiIiIioFkyBNs7KSltFgEkRERKRoTIK0YeBA4PBhIDNT7kiIiIioBEyCtGHgQCkBOnpU7kiIiIioBEyCtKFpU8DdnU1iRERECsYkSBtUKqk2iEkQERGRYjEJ0pY+fYCbN4E7d+SOhIiIiIrBJEhbunWTaoQCA+WOhIiIiIrBJEhb7OyAFi2kUWJERESkOEyCtKlHD6kmSAi5IyEiIqL/YBKkTT17AvfuSX2DiIiISFGYBGlTly6Avj6bxIiIiBSISZA2WVkBAQHsHE1ERKRATIK0rUsX4ORJuaMgIiKi/2ASpG2dOgF370oPIiIiUgwmQdrWsaP0lbVBREREisIkSNscHYHGjZkEERERKQyTIF3o1IlJEBERkcIwCdKFzp2By5eB1FS5IyEiIqL/xyRIFzp1AtRq4OxZuSMhIiKi/8ckSBeaNJHWEmOTGBERkWIwCdIFPT1plNipU3JHQkRERP+PSZCutGsHnDvHxVSJiIgUgkmQrrRtCyQlATduyB0JERERgUmQ7rRuLX09d07eOIiIiAgAkyDdsbMDPD2ZBBERESkEkyBdatOGSRAREZFCMAnSpbZtgUuXgNxcuSMhIiKq9ZgE6VLbtkB2NhAaKnckREREtR6TIF1q0QIwMGCTGBERkQIwCdIlU1PAz49JEBERkQIwCdK1tm2ZBBERESkAkyBda9MGCA/nivJEREQyYxKka61bS0tnXL4sdyRERES1GpMgXWvaFDA2lobKExERkWyYBOmaoSHQvDkQFCR3JERERLUakyA5tGrFJIiIiEhmTILk0KoVEBYGZGXJHQkREVGtxSRIDi1bAvn5nDm6DEIIXE24ihPRJ3Ar8RaEEHKHRERENYiB3AHUSs2bA/r6UpNYmzZyR6M4+ep8/HbpN3xx4gvcTrpduN3TzhMfdv4QL7V4CXoq5u9ERFQ1/CSRg6kp4OPDEWLFSM5KxpA/hmDS7kloX7899o7Zi7A3wrD7xd3wd/LHKztfwYD1A5CYmSh3qEREVM2xJkgu7Bz9lLScNAxYPwARCRHYN2Yf+jXuV/icj4MPBnkNwv4b+zF662h0W90Nh8YfgoO5g4wRExFRdcaaILm0bAmEhAC5uXJHoghCCIzZOgZX4q7gwLgDRRKgJ/Vr3A/HXz6O2PRYDN04FFl57FxORESVwyRILq1aAdnZQESE3JEowpIzS7Dz6k5seH4DWru0LnVfHwcf7By1E5diLuF/u/+nowiJiKimYRIklxYtpK9sEsPNxzfx0aGPMK39NAz2GlyuY9rVb4flg5dj7eW12By2WcsREhFRTcQkSC6WloCXV63vHC2EwJS9U+Bk4YT5PedX6NhxfuPwgs8LeH3363iY+lBLERIRUU3FJEhOLVvW+pqgv6//jX039uH7Ad/DzNCsQseqVCr8POhn6OvpY8bBGVqKkIiIaiomQXJq1UqqCVKr5Y5EFkIIfBL4Cbq6d8UQryGVOkcdszr4oucXWBeyDqfuntJwhEREVJMxCZKTvz+Qng7cuiV3JLLYcXUHLsVcwrzu86BSqSp9noktJyLAOQBT90/lrNJERFRuTILk5O8vfb18Wd44ZCCEwOfHP0ePBj3QrUG3Kp1LX08fC3otwLn757Dn+h4NRUhERDUdkyA5OTkBdevWyiTo7P2zuPDgAt7r8J5Gzte7YW90de+K2YGzoRa1s3mRiIgqhkmQ3Pz9pUkTa5nvz36PRraNMMBzgEbOp1KpML/HfFyKuYTtkds1ck4iIqrZmATJzd+/1tUEPUh9gD/D/8SUtlM0uhBqV/eu6N6gOxadWqSxcxIRUc3FJEhufn7A7dtAcrLckejMyqCVMNI3wsstXtb4ud/r8B7O3DvDkWJERFQmnSRBP/74Ixo0aAATExO0a9cO586dK3Hf1atXQ6VSFXmYmJjoIkx5FHSOriVNYkIIrA1Zixd8XoC1ibXGzz/QcyCa1GmCr09/rfFzExFRzaL1JGjTpk2YNm0a5syZg6CgIPj7+6Nfv36Ii4sr8RgrKys8fPiw8HHnzh1thykfb2/A0LDWJEFn7p3Bjcc3MM5vnFbOr6fSw9T2U7EtYhtuPr6plTKIiKhm0HoS9M033+C1117Dyy+/DB8fHyxbtgxmZmb47bffSjxGpVLBycmp8OHo6KjtMOVjZAT4+NSafkHrQtahvlV9dG/QXWtljPcfDztTO/x4/ketlUFERNWfVpOgnJwcXLx4Eb179/63QD099O7dG6dPny7xuLS0NLi7u8PV1RVDhw5FWFhYiftmZ2cjJSWlyKPaqSWdo7PzsrHxykaMbT4W+nr6WivH1NAUL7d4GWsur0FWXpbWyiEioupNq0lQQkIC8vPzn6rJcXR0RExMTLHHNGnSBL/99ht27NiB33//HWq1Gh07dsS9e/eK3X/BggWwtrYufLi6umr8OrTOzw8IDQXy8+WORKv+ufkPErMSMdZvrNbLei3gNTzOfIwt4Vu0XhYREVVPihsd1qFDB4wfPx4tWrRAt27dsHXrVjg4OGD58uXF7j9z5kwkJycXPu7evavjiDXA3x/IzARu1uw+LFsjt8Lb3hu+dX21XpZXHS/0aNADK4JWaL0sIiKqnrSaBNnb20NfXx+xsbFFtsfGxsLJyalc5zA0NETLli1x48aNYp83NjaGlZVVkUe1UwuWz8jNz8XOqzvxnPdzOitzUsAkHLtzDJEJkTork4iIqg+tJkFGRkYICAjAoUOHCrep1WocOnQIHTp0KNc58vPzERoaCmdnZ22FKT8HB8DZuUYnQcfuHMPjzMd4rqnukqBnvZ+FvZk9fg36VWdlEhFR9aH15rBp06bhl19+wZo1axAREYHJkycjPT0dL78sTZQ3fvx4zJw5s3D/efPm4Z9//sGtW7cQFBSEsWPH4s6dO3j11Ve1Haq8avjyGVsjtsLN2g2tnFvprExjA2O82OxFbAjdgHx1ze5vRUREFWeg7QJGjhyJ+Ph4zJ49GzExMWjRogX27dtX2Fk6Ojoaenr/5mKJiYl47bXXEBMTA1tbWwQEBODUqVPw8fHRdqjy8vMDNm6UOwqtUAs1tkVuw0jfkVCpVDote5zfOPxw7gccijqEvo366rRsIiJSNpUQQsgdhCalpKTA2toaycnJ1at/0IYNwJgxwOPHgK2t3NFo1KWHl9BqRSscGn8IPT166rRsIQSa/tgUbeq1wbpn1+m0bCIi0r2K5AGKGx1Wa9Xg5TP23dgHc0NzdHbrrPOyVSoVxvmNw9aIrUjLSdN5+UREpFxMgpSiSRPA2LhmJkE396FXw14w0jeSpfyxfmORkZuBrRFbZSmfiIiUiUmQUhgYAL6+NW6EWHJWMk5Gn0T/Rv1li8Hdxh3d3LthXQibw4iI6F9MgpTEz6/GJUGHog4hX+Sjf2P5kiAAGN18NA5HHUZceskL9xIRUe3CJEhJ/P2BsLAatXzG3ut70aROE3jYesgax7Pez0IFFbZFbJM1DiIiUg4mQUri5yctn1HC7NjVjRAC+27uw4DGA+QOBQ7mDujh0QObwzfLHQoRESkEkyAlad5c+lpDOkdfe3QN91LuoU+jPnKHAgB4wecFHLl9hE1iREQEgEmQshQsn1FDkqDA24HQV+mji1sXuUMBwCYxIiIqikmQ0vj51Zgk6MjtI2jt0hqWxpZyhwLg3yaxP8P/lDsUIiJSACZBSlNDkiAhBI7cPoIeDXrIHUoRL/i8gMDbgWwSIyIiJkGK4+cH3L4NJCfLHUmVRCREIDY9Fj08lJUEsUmMiIgKMAlSmoLlM65ckTeOKjpy+wgM9AzQybWT3KEU4WDugO4NurNJjIiImAQpTpMmgKFhtW8SC7wdiLb12sLcyFzuUJ7yXNPncOT2ESRmJsodChERyYhJkNIYGQFNm1brJEip/YEKPNPkGeSLfPx9/W+5QyEiIhkxCVKiar58RmRCJBIyEtDNvZvcoRSrvlV9tHZpjR1Xd8gdChERyYhJkBL5+QGhoYBaLXcklXLq7inoqfTQrn47uUMp0dAmQ7H3xl5k52XLHQoREcmESZAS+fkBaWnSKLFq6OTdk2hetzmsjK3kDqVEw7yHIS0nDYejDssdChERyYRJkBL5+Ulfq2m/oFN3TyluVNh/+Tr4oqFtQzaJERHVYkyClMjJCbC3r5ZJUEJGAq4+uoqOrh3lDqVUKpUKw5oMw46rO6AWFWh2TEsDLl4EAgOlr48fay9IIiLSKiZBSqRSVduZo0/fPQ0Aik+CAGCo91DEpMXg/P3zpe+YmQksXw506ABYWwOtWwM9e0pf69SR5nZasACI4yzURETVCZMgpaqmSdCpu6fgbOGMBjYN5A6lTB1dO6KOaZ3Sm8Q2bQK8vIA33pASnp9/Bs6dA65fBy5cANasAZo3B+bNAzw8gE8/BdLTdXcRRERUaUyClMrfH7hxo9p9oJ68exIdXTtCpVLJHUqZDPQMMKTJEGyP3P70k+npwLhxwKhRQNu2wNWrwO7dwKRJQJs2QOPGQEAAMH488PvvwP37wJtvAl98AbRqBQQF6fx6iIioYpgEKZWfHyAEEBYmdyTllpOfg/MPzleLprACQ5sMRURCBK4/uv7vxsePgd69gW3bpARnyxYp6SmNnR2wcKFUe2dhAbRvD/z2m3aDJyKiKmESpFQ+PoCeXrVqEguOCUZWXpbiR4Y9qW+jvjAxMMGua7ukDY8eAV27SrVwR44AY8ZU7IRNmgCnTgEvvwy88gowZ46UzBIRkeIwCVIqExPpA7UazRx9+u5pGOsbo6VzS7lDKTczQzP0aNADe67vATIygMGDpQ7Ox49LHZ8rw9gYWLZMahqbNw/46CMmQkRECmQgdwBUimrWOfrcg3No4dQCRvpGcodSIYO9BuOdfe8gefxIWIeESDVA3t5VO6lKBcycKSWz06ZJidHcuZoIl4iINIQ1QUpWkARVk1qE8/fPo41LG7nDqLBBnoOQp87DgYjdwB9/SB2fNWXqVGn4/KefSsPsiYhIMZgEKZmfH5CUBNy7J3ckZUrKSsL1x9fRpl71S4LcIx6gWRyw+1lf4JlnNF/Ahx8Cb70ljR47eFDz5yciokphEqRk1Wj5jAsPLgBA9asJyswEJkzA4DQX/G0dV7HZoyvim2+kEWfDh0vD7YmISHZMgpTM1VWaobgaJEHn75+HpZElmtg3kTuUivn0U+DOHQx6dSHiM+LLnj26sgwMpIkXXVykRCgjQzvlEBFRuTEJUrJqtHzG+QfnEeASAD1VNfqVungRWLwYmDMH7TuNhJ2pHXZf26298qytgT//BG7eBN5+W3vlEBFRuVSjT6xaqholQdWqKUytlvroNGsGfPABDPQM0L9xf2movDb5+gI//gisXClNxEhERLJhEqR0/v5SH5KsLLkjKVFMWgzupdyrXknQxo3A2bPAd98BhoYAgMGeg3Ep5hLup9zXbtkvvSQtyfHGG8CdO9oti4iISsQkSOn8/ID8fCAiQu5ISlTQj6bajAzLyJBGbD37LNCtW+Hmfo37QU+lh7+v/63d8lUq4IcfABsbYOJEqVaKiIh0jkmQ0vn6Sh+aCp45+vyD87A3s4e7tbvcoZTPkiVATIy01tcT7Ezt0Mm1E3Zf12K/oALW1tLaYocPSyvTExGRzjEJUjoLC6BRI0X3CyroD1QdVo5HUpLUGfr114tdFHWw12AcvHUQWXk6aH7s3RuYPBmYPl1aq4yIiHSKSVB1oODO0UIIXHhwofr0B/r+e6l/1cyZxT49yHMQMnIzcOT2Ed3Es3Ah4OQkLbbKZjEiIp3i2mHVgZ8fsHSptHyGwmpb7qbcRUJGAlq7VHKxUV1KSpKawv73P8DZudhdfBx80MCmAXZf243+jftrPyYLC+CXX4BevYDVq6U+QlQoIzcDx+8cx9E7RxGZEIno5Ghk52dDX6UPZ0tneNp5on399ujm3g31rOrJHS4RVTNMgqoDPz8gIQGIjZVqDRTk0sNLAFA9Vo4vqAWaMaPEXVQqFQZ5DsKe63vwg/hBN018PXtKo8U++AAYMgRwcNB+mQoXEhuC7858h83hm5GWkwYnCyf4OfqhpVNLmBmaISc/Bw/THmLfjX344dwPAIDObp0xzm8cxvmNg6mhqcxXQETVAZOg6uDJ5TMUlgQFxwTD3swe9SwV/l94amqZtUAFBnsNxo/nf0R4fDh86/rqJr7Fi4Hdu6VEaPVq3ZSpQDce38BHhz7Cn+F/wt3aHe93eB8jfEfA2967xIQ0ISMBf1//G5vCNmHynsn4+PDHeLfdu5jaYSrMDM10fAVEVJ2wT1B14OEBmJsrsl/QpZhLaOHUQvmdon/7DUhLA957r8xduzfoDjNDM+3OHv1fdesCixYBa9YAgYG6K1ch8tX5WHxqMZr/3Bxn75/FymdW4vpb1zGn+xw0dWha6u+XvZk9xvuPx57Re3D9resY6TsS847Ng9cPXvg95HcIIXR4JURUnTAJqg709IDmzRWbBLV0UnhTWF4e8O23wIgR0npsZTAxMEHvhr11M1T+SS+/DHTuLI1cy87Wbdkyik+PR591fTD9wHRMbj0Z4W+EY2LLiTDUN6zwuRraNsTSgUsR8WYE2tdvj3HbxqH/+v64m3xXC5ETUXXHJKi68PdXXBL0OPMxopOjlZ8EbdsG3L5drlqgAoM9B+PU3VN4nPlYe3H9l54esGwZcOuWtOp8LXDp4SUErAhAWHwYAicE4pt+38DcyLzK521o2xB/jfgLe8fsRVhcGJr93Ax/hP6hgYiJqCZhElRd+PkB4eFATo7ckRQKjgkGALRwaiFrHKUSAvj6a6B7d6BVq3IfNtBzINRCjb3X92ovtuL4+kqLq372GXDvnm7L1rFjd46h2+puqGteFxdeu4BuDbqVfVAF9W/cH6GTQzHIcxBGbx2Nt/e+jZx85fwNEZG8mARVF35+QG6utI6YQgTHBMPUwBRedbzkDqVkZ85Ia4RVoBYIAOpZ1UMr51a6bxIDgNmzpaHzpYxiq+7239iPfr/3Q9t6bXHkpSNwtS67mbKybE1tsf659Vg6YCmWXViG7qu7IyYtRmvlEVH1wSSoumjeXPqqoCaxSzGX4OfoB309fblDKdlPP0kzbg8cWOFDh3gNwb4b+5Cbn6uFwEphbQ18+SWwYQNw8qRuy9aBE9EnMGzTMKnf1ejdsDCy0HqZKpUKb7Z9E8dePoaopCh0WNkBEfHKXY+PiHSDSVB1YW0NuLsrKwl6qPBO0QkJwJ9/SsPi9Sr+qz7YazCSspJw6u4pLQRXhgkTgDZtgLfekhbQrSEux1zG4A2D0b5+e/z5wp8wMTDRafnt67fH2VfPwtzQHJ1+64Rjd47ptHwiUhYmQdWJgpbPyMzNRGRCpLInSVyzRuoT9NJLlTq8lXMrOFk4Yde1XZqNqzz09KTJHS9dAlau1H35WnA/5T76r++PRnaNsGPUDp0nQAXcrN1wYuIJtHRuiT7r+mBH5A5Z4iAi+TEJqk4UlARdibuCfJGv3E7RajWwfDkwfHilZ2DWU+lhkOcg3c4X9KT27aUaoY8+AhIT5YlBQ7LysvDspmdhoGeAv0f/DStjK1njsTGxwd4xezG0yVA8v/l5bLqySdZ4iEgeTIKqEz8/4MEDqZlHZsExwdBT6aF53eZyh1K8wEDg+nVplfYqGOI1BFcfXcX1R9c1FFgFLVggjQicM0ee8jVACIFJuyYhNC4U20duh6OFo9whAQCM9I2w4fkNGOM3BqO3jsaqS6vkDomIdIxJUHVSsHxGaKi8cUDqFO1t763cNZqWLZOGm3fqVKXT9GrYC8b6xthzfY+GAqsgZ2dptNhPPynida+M5ReXY13IOqx8ZiUCXALkDqcIAz0DrBq6CpNaTcLEnRPx8/mf5Q6JiHSIa4dVJ40bAyYmUpNYjx6yhqLomaLj44Ht26X5gaq4nIeFkQV6ePTArmu78G77dzUSXoW9/ba00vw77wCHDlX5mnTpStwVTN0/FW+0fgOjm4+WO5xi6an08NOgn2BiYII3/n4DhvqGeLXVq0/v+OCBNN3CuXPAtWvAnTvSXE4ZGdLCvCqVNIDB2lqambxxY6BJE6BtWyAgADDjOmZESsMkqDoxMACaNZO9X5BaqBESG4Lnmz4vaxwl2rBB+kAaM0YjpxvsORjv7n8XyVnJsDax1sg5K8TISFr2Y+BAYOtW4HmF3vf/yMzNxItbXkRju8ZY3Hex3OGUSqVS4Zt+3yBXnYtJuybBUM8QE/zHAxcuSDOOb98ORPz/kPp69QAfH6BlS2DIEGlOJ1NTqR9acjKQlCQlSBcvAuvXS0mSvr40WefAgcDgwdL3lRixSESaxSSouvHzAy5fljWEW4m3kJGbAT9HP1njKNHq1dKHU506GjndYK/BmLJ3Cv65+Q9e8H1BI+essAEDgEGDpEkfBw6UPnQV7v1/3seNxzdw4bULym02fYJKpcL3A75HTmYaJu54GUYfzcKLe+9Jv0dDhgCffgp06ADUr1/+k+blAWFh0qSdgYFSMvvpp1IiNWYMMH681GxLRLLgvyLVjZ+f9KaalydbCKGxUt8URXaKvnwZCA6u9LD44rjbuKN53ebyzB79pCVLpCaZRYvkjaMcDt06hJ8u/ITFfRbDt241+ZB//Bh6c+Zi2cStGHcZGNf2PrZsmAXExACrVgEvvFCxBAiQam/9/aW5qjZulJpqAwOBYcOAX3+VanZbtwZ++01qUiMinWISVN34+UlvljduyBZCaFwo6pjWgZOFk2wxlGjNGmlIfP/+Gj3tYK/B+Pv638hXyzhxoacnMHWqNJt0dLR8cZQhLScNr+16Dd0bdMfkNlUbnacT2dnSPfXwABYvht6rr2Hld7cxovkojLrxJXbe/FtzZRkaSuvYLV0KPHwoNbU5OgKvvCL1I5o1C7h/X3PlEVGpmARVNwpYPiM0LhTNHZtDpbQOurm5wO+/A2PHSh82GjTEawgSMhJw9v5ZjZ63wmbNkjrefvCBvHGU4uNDHyMmLQa/DvkVeiqFv8X8/bf0NzVrllR7GBUFfP019F3dsPbZtRjaZChe+PMF7LuxT/NlGxlJNUJ79kgdrUePlibIbNgQeP114PZtzZdZzeXm5yI6ORoXHlzA0dtHsff6XmyL2Ibd13bjwM0DOH7nOMLjw/Eo4xHUQi13uFQNsE9QdWNvD7i4SEnQiBGyhBASG4L+jTRb06IR+/ZJzQ0TJmj81G3rtYW9mT12X9uNjq4dNX7+crO0BL76SrrGyZOlWgUFORF9Aj+c+wFf9/0ajewayR1OyR49AqZMkZqoevaUamT+0zfHQM8AG57fgOGbh+PZTc9iz+g96OnRUzvxeHoC330HzJ8P/PyzNLJx5Uqpz9BHH0nr39Uiufm5CHoYhEsxlxASG4LQuFDceHwDsWmxEBDlOoeBngFcLF3gVccL3nW80cS+CZrXbY4AlwCdrFdH1YNKCFG+36hqIiUlBdbW1khOToaVlbyz0mrNgAFSTcfOnTovOjM3ExYLLLB88PLihxHL6fnngVu3pKUmtGDC9gm49PASQibLPGu3Wi3Nf5SRIY1AMlDG/zI5+TnwX+YPGxMbnHj5hHIX1t2zB3j1ValZeelSqQamlFrNrLwsDN04FCeiT2D/2P3o7NZZ+zGmp0szni9cKE2OOm4cMHeutH5gDSSEQHh8OHZe3YnA24E4dfcU0nPTYaBngCZ1msDP0Q9edbxQ36o+6lvVh6O5I8yNzGFuaA5jA2Pk5uciOz8bWXlZSMhIQGxaLGLTY3E3+S6uPrqKq4+u4sbjG8jJz4GeSg8+Dj5o69IWHV07oqdHT3jYesh9C0iDKpIHKOPdkyrGzw/YJM80/+Hx4VALtfI6RSclAbt3SzMsa8lgz8FYe3kt7iTdgbuNjB9GBeuKtW0LrFgBvPGGfLE8YcnpJbj+6DqC/hekzAQoJweYPl2qcRkwQOqY7OJS5mEmBibYNnIbBm0YhIHrB+Lg+INoW6+tdmM1NwemTZNq+375Bfj8c2nqhzfekGqGKrkUjNJcjrmMP678gW2R23Dt0TWYG5qjq3tXzO42G93cu6GFUwsYGxhrpKw8dR4iEyJx7v45nLt/Dmfvn8Xqy6uhFmp42Higl0cv9GrYC30a9kEdM82MLKVqQNQwycnJAoBITk6WOxTt+f13IQAhkpJ0XvSqS6sE5kKkZqfqvOxS/fabECqVEPfva62I5KxkYTDPQCw9u1RrZVTIxIlC2NkJkZAgdyTibvJdYf65uXhn7ztyh1K86Ggh2rcXwtBQiO+/F0KtrvApUrNTRceVHYXNlzYi6EGQFoIsrfBUIebPF8LKSggLCyHmzBGimr7HJWYmih/P/ShaLW8lMBfCfqG9eGXHK2L31d0iMzdT57Fsj9gupuyZIpoubSowF0LvUz3RdVVXsejkInE14WrFTqhWC5GdLb1eaWlC5ORU6neNqqYieQCbw6qj0FCpNuj4caCzDqrmn/De/vew/ep23Hz7pk7LLVPfvlLH6MBArRbTe21vGOobYu+YvVotp1xiYwEvL6kj+I8/yhrKqL9G4cjtI7g65ao8E0qW5vBhqf+cuTmweTPQrl2lT5WclYw+6/rgVuItHHnpCJrVbabBQMvh0SNpJNvSpdIkjR9/LHWiNjHRbRyVcO3RNSw5vQRrLq9BTn4OBnsNxsSWEzHQcyAM9JTRKHE/5T7+vv43dl7biYO3DiIrLwtNbBpjiE07DBVe6BBrBP3ou9Lf3qNHwOPH0tfkZKmmMSfn6ZOqVFIneGNjaVCDrS1gZyd9rVNHqo2sX1+aO6p+felha1utZoZXmorkATpJgn788UcsWrQIMTEx8Pf3xw8//IC2bUuuTv7zzz/xySef4Pbt2/D09MRXX32FgQMHlqusWpEE5eZKb+jffqvzppC+6/rC3Mgc20Zu02m5pYqNld5IfvpJmo9Fi7498y1mHJyBhA8SYGlsqdWyyuWbb6SRYpcu/bu2nI4FRgWi59qeWDNsDcb7j5clhhL98ov0N9KjB/DHHxqZQDMxMxE91/bEg9QHOPbSMTSxb6KBQCvo3j1g3jxpfiEXF2mB3QkTFNM/7Emn7p7CwpMLsfPqTjiYO2BKmyl4LeA15U2xkZYGBAVJ/2SGhiIj/DIOpoVgp2sGdnsBsRaAQ4YKz8TaYGiWO3rrNYapnaP0O2VtLSU5BclOwejUgsQoJ0fqg5aUJCVOiYn/JlAPHkjTJTz5UWxhIS274ukpfX3yeycnJkhlqFAeoOVaKbFx40ZhZGQkfvvtNxEWFiZee+01YWNjI2JjY4vd/+TJk0JfX18sXLhQhIeHi1mzZglDQ0MRGhparvJqRXOYEEL4+wsxaZLOi3Va7CQ+OfyJzsst1dKlQhgY6KRZKCoxSmAuxKYrm7ReVrlkZwvRpIkQ3brJUu2ek5cjfH70EZ1WdhJqJVX75+UJ8d57UrPxG28IkZur0dPHpcUJnx99hMvXLuLGoxsaPXeFXL0qxIgR0nU2bizE+vXStSvAmbtnRJ+1fQTmQvj86CN+vfirzpu7SqRWCxEZKcSqVUL873/S+6mennQfDQ2FaN5ciNGjhfjiCyG2bhX5QRfFqfD9YsaBGcLrBy+BuRBmn5uJ5zY9J9YGrxWPMh5VLZ6cHKnJ9tQpITZvFmLRIun9vWdPIVxdpbgKHhYWQrRqJcSLLwoxd64Qf/whxMWLUhMcCSEU1hzWrl07tGnTBkuXLgUAqNVquLq64q233sKHH3741P4jR45Eeno6du/+d3be9u3bo0WLFli2bFmZ5dWKmiBAGjp7/Tpw+rTOioxPj0fdxXWxefhm+ZaPKE7nztJ/Ynt0s9J7q+Wt0MS+Cf54/g+dlFemffukjr5//AGMGqXTor8/+z2m7p+Ki5MuooVTC52WXaL0dGlJil27pFm233pLK/85x6TFoNvqbsjKy8Kxl47J21n+8mVg9mxpxKivr1RL9OyzstQYBD0MwuzA2dhzfQ98HXzxafdP8WzTZ+WfMyoxEThwQPp72bdPqn1RqaR14Nq3lx7t2gHe3mXOMxaZEIntkdux4+oOnLl3BvoqfXR174ph3sMwtMlQzf8uZGZKI1+vX5ceV69Kc0tdvQrExf27X7160qK9BQ8vL+mru7u0fp2MUrNTER4fjitxVxCZEInrj6+jo2tHTO80XeNlKWZ0WE5ODi5evIiZM2cWbtPT00Pv3r1xuoQP79OnT2PatGlFtvXr1w/bt28vdv/s7GxkZ2cX/pySklL1wKsDPz9pMU21WmcLMYbG/f9yGY4KGhkWHQ2cPAmsW6ezIp/1fhaLTi1Cdl62xkauVEn//sBzzwHvvgv06yf1J9CBlOwUzD82Hy+3eFk5CVBysrTGWnCwlBAMGqS1opwsnHBo/CF0XdUVPdf2xJEJR+Bq7aq18krl7w/s2CGtcP/JJ9J0ES1bAp99JiXIOkiGbifdxoyDM7A5bDM87Tyx/rn1GOk7Ur6Rgmq11Ly1bx+wd6+0fptaLSWJo0cDffpIiY91xfuwedt748POH+LDzh/iYepD7Ly6Ezuu7sAHBz7AO/veQQunFhjWZBiGeQ+Dn6Nf1SeWNTWV4i5unbnExH8TooLk6MQJaamXgqVYjI2lprQnE6OCh51d1WL7j6y8LEQmROJK3JXCR1h8GG4n3QYAqKBCA5sG8KrjBStj+SsqtJoEJSQkID8/H46OjkW2Ozo6IjIysthjYmJiit0/Jiam2P0XLFiATz/9VDMBVyd+ftJ/vFFROptILTQ2FMb6xmhs11gn5ZXLxo1Sp9ChQ3VW5LNNn8XsI7NxKOoQBnqWr6+a1n3/PdC0KfDhh9L8Mjqw+NRipOWkYW73uTopr0zx8VJCeOsWcPCg9AGnZfWt6uPwhMPosaYHOq/qjIPjDsKzjqfWyy1R27bA/v3AsWPSLNiDBgEBAdLUAM89p5U+Q6nZqVhwYgG+Of0N7EztsPKZlRjvP16ezs7x8cA//0iJz/790s9WVkDv3sCyZdLvh6tmE1VnS2f8r/X/8L/W/0NKdgr23diH7ZHbseTMEsw9Ohfu1u4Y5j0MfRv1RRe3LprvS2hrK9Vg/bfDv1ot/ZP4ZHJ09Sqwfj1w9+6/+9nbF02OPD2lfmbOzlL/I+Pi/9HLzc/F9cfXpSQnLgxX4qWE58bjG4WzdbtZu8HXwRcv+LyAZnWbwdfBF00dmsLM0Eyz96AKlNeLroJmzpxZpOYoJSUFrhr+JVekgk6wISG6S4LiQuHj4KOYkRwApCagwYOlmZR1xNfBF552ntgasVU5SVC9etIcSVOmSBPraXnUYExaDL4+/TXeafcO6ltVcFFRbbh/X/rP/tEj4MgRqWZERxrYNMDxl4+j99re6LKqCw6MOyB/bWnXrsDRo8ChQ9JospEjpeU43nsPePllqWahivLV+VgdvBofH/4YydnJmN5pOqZ3mq7b2Zjz86Xar717pcTnwgWp50zLltKEmP37Ax06aHwZnZJYGVthhO8IjPAdgZz8HBy9fRTbI7djS8QWfHf2O+ir9NHapTV6NOiBHh490KF+B+0NsNDTAxo0kB79+hV9Lj1dalZ7sgYpNBT46y8gNbXIrnl1bHGzcR2ENzBDWB01wiwzEWacgki9x8iFtJaik4EtfM3cMcCiGZp5DYWvjSd8bL1gbWwtLfadnw+k5wMpGcDVs9K2rCwp2QoI0M71l5NWP83s7e2hr6+P2NjYIttjY2Ph5FT8yAAnJ6cK7W9sbAzjEjJVbRFCyL9ulqOjNGFacLDU9q8DoXGh8HOUZwRSsSIjpev/5BOdFqtSqfCs97NYFbwK+ep85UwM+PrrUrPg//4njRYzMtJaUfOOzoOxvjFmdJqhtTLK7dYt6T/93FypBqSJ7kdr1beqj2MvH0O/3/uh2+pu2Dd2n/YnVCyLSiXdl969pZnFFy2S+kfNmQNMnAi89prURFIJgVGBmPbPNATHBGN089FY0GsB3KzdNHwBJXj4UKrl2bdPqvVJTJRqQ/r2Bd58U/rq7KybWEphpG+EPo36oE+jPlg6cCmuP76OwKhABN4OxKrgVfjy5JdQQQVve2+0qdcGrZ1bo7VLa/jW9dV+M5G5OdCihfT4f6nZqbj1+CZu3rmE8OiLCIu7gvCUW4jMfYAcJAIA7HIN4Jtigs7Renj9oQl8o7PgG5MP+4xEAIkAgisWx/jx0qLXMtJJx+i2bdvihx9+ACB1jHZzc8OUKVNK7BidkZGBXbt2FW7r2LEj/Pz8ZO8Yna/Oh+1XtljSbwleafWKRs9dKf37S//hPHGvtEUt1LBaYIVPu3+K9zq+p/XyymX+fGlZgfh4nc+TcubeGXRY2QFHXzqKru5ddVp2qUJCpP+s5syRmkO04Pqj6/D5yQdf9PwCH3SSeSHX8HCpBsjMTGoCk3lZiaSsJAxcPxChcaHYNHyTcmoKC9y6JTWdrlkjDdfu1QuYNAl45ply/Q3deHwDHxz4ANsjt6NdvXb4tv+3aF9fy82OWVlSH5cDB6SkJzhYSvDatJHeAwcMkL6XueNvRQghEJEQgTP3zuDCgws4/+A8LsdcRq46FwDgbOEMb3tvNKnTBA1tG8LF0gX1rOrBxdIFThZOsDCyKHdH83x1PlJzUpGQkYCHqQ8RkxaDmLQYPEx7iNtJt3Er8RZuJt5EQkZC4TF2pnbwdfCFj4MPfB184VtX+t7R3LFoBYAQ0vI9mZlFpwMoeOTnS02wBgbS66Ov/+/PJibSVADm5hq9t4CCOkYDwLRp0zBhwgS0bt0abdu2xbfffov09HS8/PLLAIDx48ejXr16WPD/yx2888476NatG77++msMGjQIGzduxIULF7BixQpth1omfT19GOgZID4jXu5QJAEBUuc3HYhKjEJ6brr81fxP2rJFagqTYaK4tvXawsXSBVsjtiorCfLzA95/X0oQn39e6iekYbMCZ8HJwglT2k7R+LkrJChIquZ3cpI+IEuoLdYlGxMbHBh3AKO3jsaQP4bg+/7f4822b8od1r8aNpTmF1uwQGr6WL5caiqztJQSoREjpJqU//xNpWSn4PNjn2PJmSVwtHDE+ufW48VmL2qnRjw/H7hyRWrK++cfqVkvK0t6ffv0kebF6tOnWi8dolKp4OPgAx8HH0xsOREAkJ2XjStxVxCREIGrCdJ6ZyfvnsSGKxuQkv30gB9zQ3NYGlvCwsjiqS4KOfk5SMtJQ2p2KjLzMp861kjfCE4WTnC3dkdTh6YY5DkIDW0bopFdIzS0bQgHM4fyvbYqlZTEaCGR0RWtJ0EjR45EfHw8Zs+ejZiYGLRo0QL79u0r7PwcHR0NvSdGN3Xs2BEbNmzArFmz8NFHH8HT0xPbt29Hs2Y6npm1BHXN6yIuPa7sHXUhIAD44gupeljL1b8hsdKioYpZM+zmTWlYsJZqO8qip9LDsCbDsC1yG5b0WyJ/8+iTZs+WVkUfPx44dUqj/SHO3z+PzWGb8dszv8HUsOr9SirtxAmp02+TJlKziIZHuFSFuZE5to7Yivf/eR9T9k7B9cfX8XXfr5XTbApIfYLGjZMeV69KM2lv3ix1mrWwALp3B3r3Rn6vHlidcw4fH56FlOwUzOo6C+93fF+zHVuTk6WE9uRJ6XU9fRpISZESsa5dpRFuffsCzZrV6EkCjQ2MEeASgACXp/vIpOWk4UHqAzxIfYCYtBikZqdKSU5OKlKzUws7Ihcw0DOApbElLI0sCxMlBzMHOFk4wcnCCTYmNsp6z5IRl82ooC6ruqCBTQOse1Z3Q7JLdPs24OEhLRyqxaHAADD/6Hx8d/Y7xH8Qr4w/nkWLpCaf+HjZ/gs5eOsg+qzrg4uTLqKVcytZYijRuXNAx45SQjR7tkZOKYRAr7W9EJceh8uvX5bvQ33/fqkfXNu2UlOwDjvFV9RP53/CW3vfQp+GffD7c7/D3sxe7pBKFx4uDbU/cADHo4/j3V55CHIBRsc54UurZ+Haops0EMPDQ0o8y/teIAQQEyONZo2KkjrkXr4sPW7flvaxtgY6dZIenTtLTVwa6MBNtY+imsNqGkXVBLm7S29EFy9qPQkKTwiHb11fZSRAgNQU1r+/rNWw3dy7wdbEFn+F/6W8JKhtW2ldqfnzgYEDgdatq3zKf27+g8Dbgdg5aqd8CdDWrdKEkH36SM05Cv+QfKPNG/Cq44UXt7yIlstbYvPwzejg2kHusErm44ObTsb4yDMYm8Py0NrcCyczuqLj/Xhg5y7gy5//3dfSUhqgYW0tPSz+f1SYENLw7LS0f5eISEj4d84aAKhbV2q6ff55aSRfy5bSpIU6mvOMqACToApyMHNAVGKU3GFIVCqpSeziRa0XFR4fjo71O2q9nHK5dw84exb4/XdZwzDUN8RzTZ/D5rDN+Lzn58pJEAvMmiXVEo4fL/2OVCFhUAs1Zhycgc5unTHYa7AGg6yAtWul4d3Dh0uj4LQ4+k2TejfsjeD/BWPkXyPRdXVXfNr9U0zvNF1ZU01AmvZg/tH5WBG0AnXN62L10NUY5z+uaAfcx4//rc2JipKSm6QkqUkrNVVKYvT0pI6v9eoBzZv/u1BogwZSDVKDBtLcPUQKoKy/wmpAUTVBANCqldSOr0V56jxcTbiKV1u+qtVyym3rVqmfy2CZPoyfMKrZKKy8tBIXH15Ea5eq17ZolKGhlCy0aiXND/PTT5U+1R+hf+By7GWcnHhSnmTvxx+lOZBeeUXqzFuNRgIBQD2regicEIg5R+bgk8BPsDViK1YPW637VeiLkZSVhMWnFmPJmSUw0jfC5z0/x5S2U4rv92NnJz1kntuFSFNY91hBdc3rIj4jHorpShUQINWMxGkvMYtKjEJ2fjZ8HHy0VkaFbNkizX1SienuNa17g+5wMHPApiub5A6leD4+0pDon38GNmyo1Cmy87IxK3AWhnkPQ0dXHdcGCiF1jJ0yRVoW5Jdfql0CVMBQ3xBf9PoCp185jcy8TLRa3gozD84sduSPLsSkxeDDgx/C/Vt3fHP6G7zT7h3cevsWpnearqgZfYm0iUlQBTmYOSAnP0e2N66ntPr/vihabBILiw8DAPjWLWbdGl2LjQWOH5f6EiiAgZ4BXvB5AZvCNj01QkMxXntNWlB00iQgIqLChy+7sAzRydH4oucXWgiuFEJIw/0/+QT49FPgm29qxOigtvXa4uKki/ioy0f47ux38PzBE8suLEN2XnbZB2vAlbgrmLx7Mhp82wA/nf8Jrwe8jlvv3MIXvb6Aralu1p0jUgomQRVU17wuACinSaxhQ8DGRqtJUHh8OGxNbOFo7lj2ztq2fbvU50CHa4WVZVSzUbibchdn7p2RO5TiqVTSuklublJ/mvT0ch+akp2Cz45/hoktJqKpg+bnHCpRXp607ME330g1WbNn14gEqICJgQnmdp+La29dQ79G/fDGnjfQ8PuGWHRyEZKzkjVeXlpOGtZdXofOv3VG85+bY1vkNnzS9RNET43GV32+gpOF/HMsEcmBSVAFOZhLE3QpZsJElUqqDQoK0loR4fHh8HHwUUbH361bgW7dpEX/FKKTWyfUs6yHjVc2yh1KySwspNFUd+5ItUL5+eU6TJZFUrOzpQn81qyR+jS99Zbuytax+lb1sfbZtQh/Mxz9G/XHx4c/htPXTnhxy4vYfW03MnIzKn3uuPQ4bAjdgOc2PQeHRQ4Yv308TAxM8OcLfyJ6ajQ+7voxbExsNHcxRNUQO0ZXkOJqggApCdq8WWunD48PV0an38RE4PBh4Lvv5I6kCD2VHkb4jsAfV/7Akn5LlDUp3pN8fICNG6VatOnTga+/LnX3JxdJrWdVTzcxJiZKq52fPi1N+DhkiG7KlZm3vTdWDl2J+T3nY93ldVhzeQ02XtkIY31jdHbrjHb12qGFUwt41vGEk4UT7M3soa+Sfs+SspKQkJGAuyl3ERYXhtC4UJy6e6qwGbuNSxvM6z4Pw32Gw8PWQ87LJFIcJkEVVMe0DlRQIT5dITVBgNQ5evFiabiqhmtI8tX5iEiIwHj/8Ro9b6Xs3CnVYOhowdiKGNVsFJacWYKjd46ip0dPucMp2eDB0rIJb78tLZ45eXKJu+p8kdRbt6T5ruLipGUwunTRTbkK4mLpghmdZ2B6p+mITIjE/pv7cfDWQay+vBoPTjwo83gjfSN423ujff32mNl5Jro36K67BJaoGmISVEH6evqoY1ZHWTVBBcNVg4Kk6eU16HbSbWTlZcHXQQGdordsATp0UMQK0f/VxqUNGtk2wu8hvys7CQKk5qUbN6QRVzY2wIsvPrXLtUfXsOLiCnzZ+0vddJY9fVqqobK2Bs6cATw9tV+mgqlUKjR1aIqmDk3xbvt3AUi1z7eTbuNh6kM8znwMtVBDLdSwMbGBg7kDXCxd0NC2oeLmHyJSMv61VIKDmYNy+gQB0jT2lpZS52gNJ0Hh8eEAIP/w+NRUaTHFL3Q8QqmcVCoVxvuPx6JTi/DDgB9gbqTwBQWXLJEmuRs3TppPaPjwIk/POjwLLpYuulkk9bffgDfekJZJ2LZNUf29lKSued3C5ngi0gx2jK4ExU2YqKcn9Qu6cEHjpw6PD4eVsRVcLF00fu4K2bNH6jD73HPyxlGK8f7jkZaThq0RW+UOpWx6elLyMWKEVBP0xBxC5+6fw5/hf2Jej3kwMTAp5SRVlJUlDd9/5RUpGTtwgAkQEekUk6BKcDBXWE0QIK0Vde6cxk8bnqCQkWFbt0rNfg0ayBtHKRrYNED3Bt2x5vIauUMpH319aSmK0aOlEWMLF0KopeUxfB18Mc5vnPbKjoyUFspctw5YuVKaBNFEiwkXEVExmARVQl0zhdUEAUC7dtLM0Q/K7jxZEWFxYfL3B8rMBP7+WzETJJZmgv8EHI46jDtJd+QOpXwMDIDVq6V1xmbMwP63B+LI7SP4sveX2hnlplZLo/tatpQW2Dx1Cpg4UfPlEBGVA5OgSnAwd1DW6DBASoIAaWFRDVELNSISIuTvD7R/vzTBXzVIgob7DIeZoRnWhayTO5TyU6mA+fORv/JXTBf/oEuCOQblNdR8OZcuAV27SstfTJok/Vww4zkRkQyYBFWC4tYPA4D69QEXF40mQdHJ0cjIzZA/CdqyBWjWDPDykjeOcrAwssDzPs9jzeU1yvr9KId1rfQRWldgcZA9VC1bSstVZGZW/cR37khJT0CANA9QYKBUG2TG9amISF5MgirBwcwBeeo8JGUlyR1KUe3aaTQJUsTIsJwcYNcuRXeI/q+JLSbixuMbOHL7iNyhlFtmbiZmHZ6FEb4j0PZgBPDhh8DChdJcQkuWVGipDQDSul+XLkmdnhs3lvp0LVkCBAcD3btr4xKIiCqMSVAlKHLWaEBKgi5cKPeSCGUJjw+HhZEFXK1cNXK+Sjl0CEhOrhZNYQW6undFU/um+PnCz3KHUm7fnf0Ocelx0iKppqbSgqVhYdKUC9OnA05O0giurVuBmJjiT5KeDpw4AcyZA7RoITV17d0LfPklcPs28M470nB8IiKF4DxBlfDk+mFN0ETmaJ7Qrp3U2TQ8HGjevMqnC4sPk39k2JYtUk2CBq5HV1QqFV5v/Tre++c9PEx9CGdL5U3u+KSEjAQsOLEAk1tPRiO7Rv8+0bgxsGoVMHeuNIpswwbg99+l5xwcAEdHaX6qrCxptvK7d6XnbG2BPn2Azz8H+veXOl8TESkQ350qQbE1Qa1bS/O/nD2rkaShYOFU2eTlATt2SE0qcg/Rr6Dx/uMx89BMrLy0ErO6zpI7nFJ9duwzACg5Tnd3qX/QJ59IIxDPnAEiIoDYWKn2x9RUSny8vKS+Wy1aSMPviYgUjklQJdiZ2kFPpae8EWIWFoCvr5QEvfpqlU4lhEB4fDiGNx1e9s7acvy4VMNQjZrCCtiY2ODFZi9ixcUVmNl5pmIXVb35+CZ+Ov8TPu3+aWENZ6nq139qdmkiouqKfYIqQU+lB3sze+XVBAEa6xx9L+Ue0nLS5K0J2rIFcHOTariqocmtJ+Nuyl3surZL7lBK9MGBD1DXvC7eaf+O3KEQEekck6BKUtz6YQXatZM6tKalVek0so8MU6ulTrjPPVftmsIKBLgEoJNrJ3x9+mu5QynWgZsHsC1yGxb3XQwzQw5XJ6Lah0lQJSlu/bAC7dpJCcTFi1U6TVh8GMwMzeBu466hwCrozBng4cNq2RT2pA86foAT0Sdw+u5puUMpIjc/F+/sewdd3LpgpO9IucMhIpIFk6BKUuT6YQDg4yP1Dapik1h4fDia2jeFnkqmX5EtW6Rh2R07ylO+hgxpMgRN6jTBolOL5A6liB/P/4irj67i+wHfy78uHBGRTJgEVZIi1w8DpFE5bdpIazJVgawjw4SQkqBnn5VGu1Vjeio9vNfhPWyP3I5rj67JHQ4AaVTjnCNzMKnVJLRwaiF3OEREsqnenzAyUuT6YQU6dwZOnpSSiUooGBkmWxIUFCQttVDNm8IKjPMfh7rmdfH1KWX0Dfrw4IfQV+ljfs/5codCRCQrJkGVVLB+mFqo5Q7laV26SEPLr16t1OEP0x4iOTtZviRoyxagTh2gWzd5ytcwEwMTTOswDb8F/4aoxChZYzkcdRirglfhy95fwt7MXtZYiIjkxiSokuqa14VaqPE487HcoTytfXupGen48UodHhYXBgDwdfDVZFTlU9AUNnRojZpp+M02b6KOaR3MOzZPthgyczMxadckdHXvildbVW0eKSKimoBJUCU5WTgBAGLSSlhHSU6WltKsvSdOVOrw8PhwmBiYoIFNA42GVS5hYcC1azWmKayAuZE5Pu7yMdZeXovIhEhZYvj06Ke4l3IPKwavkK/DOxGRgvCdsJIUnQQBUpNYJWuCwuPD4W3vLc8sx1u2AFZWQK9eui9byyYFTEI9y3r4JPATnZcd9DAIi08txqyus9DEXkHr3RERyYhJUCU5mjsCUHAS1LkzEBUF3L9f4UPDE2TsFL1lCzBkCGBsLE/5WmRsYIzPe36Ov8L/QmBUoM7KzcjNwOgto+Hn6IfpnabrrFwiIqVjElRJ5kbmsDCyQGxarNyhFK9zZ+lrBZvEhBAIiwuTpz/Q9etAaGiNawp70li/sejk2glv7X0Lufm5Oinzvf3vITo5Ghue3wAjfSOdlElEVB0wCaoCJwsn5dYEOTkBjRtXOAmKTY9FYlaiPDVBW7YAZmZAv366L1tHVCoVlg5cioiECCw9t1Tr5e26ugvLLi7D132/hre9t9bLIyKqTpgEVYGThRNi0hWaBAGV6hck65phW7YAAwdKiVAN1sKpBSa3noxPAj/Bzcc3tVbOjcc3MH77eAzxGoLXW7+utXKIiKorJkFVoOiaIEBqEgsJAZKTy31IeHw4jPSN0NC2oRYDK8atW8CFC8Dw4botVyZf9v4SjhaOGL99PPLV+Ro/f1pOGp7d9CwczByw9tm1XBqDiKgYTIKqwMlc4UlQ167SvDsVaBILjw9HkzpNYKCn4zl6Nm2SaoAGD9ZtuTKxMLLA2mFrcebeGXx+/HONnjtPnYdx28bhdtJtbB+1HTYmNho9PxFRTcEkqAqcLJyU2zEaABo1AlxdgUOHyn1IeHw4fOvK0Cl640bgmWcAc3Pdly2TTm6dMKfbHMw9Mhe7ru7SyDmFEJi8ezJ2Xd2Fjc9vlG+UHxFRNcAkqAocLRyRkJGgs1E+FaZSSfPtVCAJCosPg4+9jj84IyKkZruRI3VbrgLM6joLw7yHYczWMQiOCa7SuYQQ+ODAB/j10q9YNXQVBnkN0kyQREQ1FJOgKnCycIKAQHyGQhdSBYDevaUEI67sFe/j0+ORkJGg+9qDTZukCRL799dtuQqgp9LD2mfXool9E/Re2xuXYy5X6jx56jy8tus1fH36a/ww4AeM8x+n4UiJiGoeJkFVoPhZowGgZ0/p6+HDZe4qy8gwIaQkaNgwwMREd+UqiIWRBf4Z+w8a2DRAz7U9KzyRYmxaLAasH4DVwauxdthaTGk7RUuREhHVLEyCqqBaJEHOzoCPT7maxMLjw2GoZ4jGdo11ENj/CwkBIiOBUaN0V6YC2Zra4sC4A2jp1BJ91vXBvKPzkJ2XXeoxQghsDtuMFstbIDQ2FP+M+4c1QEREFcAkqArqmtcFAGV3jgakJrFyJkFedbxgqG+og6D+38aNgJ2dFGMtZ2tqi31j9+HDzh9i/rH58PnJBz+c/eGpJPtx5mOsu7wO7X5th5F/jUS7eu0Q/Howenr0lClyIqLqScfjoGsWI30j1DGto+yaIEDqHP3999JcPA1Lnv8nLD4MTR2a6i6ugqaw558HDHWYeCmYgZ4BPuv5GV5s9iLmHZuHqfun4u19b8PVyhV1zOogMTMR0cnREBDo3bA3Dow7gN4NmUASEVUGk6AqcrRwVH4S1K0boKcn1QaVkgSFx4frdmbhs2elRV5reVNYcXzr+mLT8E2ITYtF4O1AhMaGIjErETYmNvCq44VeHr3gau0qd5hERNUak6AqUvzSGQBgbQ20awfs3w+89lqxuzzKeITY9FjddopeuxaoX19K0qhYjhaOGNVsFEY1Y6JIRKRp7BNURYpfOqPAwIHAP/8AOTnFPh2REAFAhyPDsrOl/kBjxwL6+ropk4iI6AlMgqrIyVzhs0YXGDwYSE0tcQmN8Phw6Kv04WnnqZt49uwBEhOBcRzNRERE8mASVEXVpibI3x+oVw/YvbvYp8Pjw+FZxxPGBsa6iWftWqB1a2n4PhERkQyYBFWRo4UjkrOTkZmbKXcopVOppCaxPXuKfTosPkx3TWEJCVIc48frpjwiIqJiMAmqooIJE2PTq0GT2KBBwLVrwPXrTz0VHh+uuzXDNm6UvnJUGBERyYhJUBVVi1mjC/TqBRgbP1UblJSVhAepD3RXE7RqlVQr5eCgm/KIiIiKwSSoigprgqpD52gLC2ktse3bi2yOiNfhyLCLF4GgIODVV7VfFhERUSmYBFWRvZk99FX6eJD6QO5Qymf4cODYMeDhw8JN4fHh0FPpwauOl/bLX7FC6qA9YID2yyIiIioFk6Aq0lPpwdnSufokQcOGSfPybN1auCk8PhwNbRvC1NBUu2WnpgIbNki1QAacp5OIiOTFJEgDXCxdqk8SVLBY6Z9/Fm7S2ciwjRuBjAxg4kTtl0VERFQGJkEaUM+yHh6kVZMkCABeeKFIk5jORoYtXy41g7m5ab8sIiKiMjAJ0gAXSxfcT7kvdxjl90STWEp2Cu6m3IVvXV/tlnnunNQpetIk7ZZDRERUTkyCNKBaNYcBUpNY377A+vWITIgEoIORYUuWSCvYDxqk3XKIiIjKiUmQBtSzrIdHmY+QlZcldyjlN2ECcPo0wkMOQQUVvO29tVfW3btSH6R33+ViqUREpBhMgjTAxdIFAPAw9WEZeyrI0KGAnR3CT25HA5sGMDM0015ZS5dKcxS9/LL2yiAiIqogJkEaUM+qHgBUryYxY2NgzBiE3w+Gj31T7ZWTlibNDfTaa1IiREREpBBMgjSgoCbofmo16hwNABMnIsw6Bz4pRtor46efgPR04K23tFcGERFRJWg1CXr8+DHGjBkDKysr2NjY4JVXXkFaWlqpx3Tv3h0qlarI4/XXX9dmmFVmbWwNUwPT6lUTBCDdxxO3bQGf41e1VEA6sHix1AzGYfFERKQwWk2CxowZg7CwMBw4cAC7d+/GsWPHMKkcQ6Rfe+01PHz4sPCxcOFCbYZZZSqVCvWs6lW7JKhwZNixCODyZc0X8PPPQGIiMHOm5s9NRERURVpbuyAiIgL79u3D+fPn0bp1awDADz/8gIEDB2Lx4sVwcXEp8VgzMzM4OTmVq5zs7GxkZ2cX/pySklK1wCvJxdKl2jWHhceHAwCaGtcDvv1WWt1dUzIygEWLgJdeAho00Nx5iYiINERrNUGnT5+GjY1NYQIEAL1794aenh7Onj1b6rHr16+Hvb09mjVrhpkzZyIjI6PEfRcsWABra+vCh6urq8auoSLqWVa/mqDw+HC4WbvBcvK7wPr1wAMNxr94MZCUBHz0kebOSUREpEFaS4JiYmJQt27dItsMDAxgZ2eHmJiYEo8bPXo0fv/9dwQGBmLmzJlYt24dxo4dW+L+M2fORHJycuHj7t27GruGiqh2s0YDCE8IlyZJLBi59fnnmjnxvXvAV19J8wJ5eGjmnERERBpW4eawDz/8EF999VWp+0RERFQ6oCf7DDVv3hzOzs7o1asXbt68iUaNGj21v7GxMYyNjStdnqYUzBothIBKpZI7nHIJiwvD0CZDAWtrYMYM4JNPgPffr3riMnOmlFR9/LFmAiUiItKCCidB7733Hl566aVS92nYsCGcnJwQFxdXZHteXh4eP35c7v4+ANCuXTsAwI0bN4pNgpSinmU9pOemIzUnFVbGVnKHU6bM3EzcSrz173IZU6ZIS1t8/DGwYUPlT3zgAPD778CvvwJWyr8PRERUe1U4CXJwcICDg0OZ+3Xo0AFJSUm4ePEiAgICAACHDx+GWq0uTGzKIzg4GADg7Oxc0VB1qnCuoJT7sHJQ/of/1UdXISD+TYLMzYEvv5SGs0+cCPTuXfGTpqYCr74K9OwpnYOIiEjBtNYnqGnTpujfvz9ee+01nDt3DidPnsSUKVMwatSowpFh9+/fh7e3N86dOwcAuHnzJubPn4+LFy/i9u3b2LlzJ8aPH4+uXbvCz89PW6FqRHWbNbpwZJjDE7NFT5gAdOsGTJ4szfFTEUJIxz16JNUCVZMmQSIiqr20Ok/Q+vXr4e3tjV69emHgwIHo3LkzVqxYUfh8bm4url69Wjj6y8jICAcPHkTfvn3h7e2N9957D88//zx27dqlzTA1wtlCqqmqLsPkw+PD4WLpAhsTm383qlTA8uXAw4fA669LiU15/fSTNMLsl1/YGZqIiKoFrc0TBAB2dnbYUEr/kgYNGkA88UHr6uqKo0ePajMkrTE1NEUd0zq4l3JP7lDKJSw+7N+msCc1aSKt9TVmDBAQII3wKsuffwJvvy09XnxR47ESERFpg1aToNrG1doVd5PlGaJfUWFxYRjkOaj4J0ePBoKDgalTAUND4M03Sz7RunVS/59Ro4BvvtFKrERERNrABVQ1yM3aDdEp0XKHUaaM3AzceHwDzeo2K3mngnl+pkyRZn3+79xOMTFS8jN+PDB2LLBmDaCvr82wiYiINIo1QRrkauWKY3eOyR1GmSLiIyAg0Nyxeck7qVTSkHl/f2DaNOCPP6RO0/XrA9HRwNGjgKWl1HT26qvsCE1ERNUOa4I0yM3aDdHJyq8JuhJ3BQCK7xP0Xy+9BNy8KdUMGRkBYWHScPqvvwZu3JBmm2YCRERE1RBrgjTI1coVydnJSMlOUfSEiaFxofCw8YCFkUX5DrC1lZrGytNJmoiIqJpgTZAGuVm7AYDiO0dfibtSelMYERFRLcAkSINcraUV7JXeJBYaF4pmDqV0iiYiIqoFmARpkIulC/RUeribotyaoMeZj/Eg9QFrgoiIqNZjEqRBBnoGcLF0UXRNUFhcGACUPjyeiIioFmASpGFu1m6KrgkKjQuFoZ4hvOp4yR0KERGRrJgEaZirlauia4KuxF1BE/smMNI3kjsUIiIiWTEJ0jA3azdFjw67EncFzeuyPxARERGTIA1ztXLF3ZS7UAu13KE8RQghjQxjfyAiIiImQZrmZu2GnPwcxKfHyx3KUx6kPkBSVhKTICIiIjAJ0jglzxVUsFwGm8OIiIiYBGlc4azRChwhFhoXCnNDc7jbuMsdChERkeyYBGlYHdM6MDUwxZ2kO3KH8pQrcVfQrG4z6Kn4shMREfHTUMNUKhXcbdxxO+m23KE8hZ2iiYiI/sUkSAs8bDwQlRQldxhF5KnzEB4fziSIiIjo/zEJ0oKGtg0VlwRdf3QdWXlZaOHUQu5QiIiIFIFJkBZ42HggKjEKQgi5QykUHBMMAPB39Jc3ECIiIoVgEqQFHrYeSM9NR0JGgtyhFLocexlu1m6wNbWVOxQiIiJFYBKkBR42HgCgqCax4Jhg1gIRERE9gUmQFnjYSknQrcRbMkfyr8uxl9kfiIiI6AlMgrTAxsQGNiY2iEpURk1QbFosYtJiWBNERET0BCZBWqKkYfKXYy8DAGuCiIiInsAkSEuUNEw+OCYYFkYWhc10RERExCRIawqGyStBQadoLpdBRET0L34qaomHrQeik6ORr86XOxRcjr3M/kBERET/wSRISzxsPJCrzsX91PuyxpGZm4nIhEj2ByIiIvoPJkFa0tC2IQDg5uObssYRFh8GtVDD34k1QURERE9iEqQlHrYe0FPp4frj67LGERwTDD2VHhdOJSIi+g8mQVpipG8EDxsPXHt0TdY4gmOC4VXHC2aGZrLGQUREpDRMgrTIs46n7DVBFx9eRIBzgKwxEBERKRGTIC3ysvPC9UfyJUF56jwExwSjtUtr2WIgIiJSKiZBWuRZxxM3E2/KNkw+PD4cWXlZrAkiIiIqBpMgLfKq44Wc/BxEJ0fLUv6FBxegggotnVvKUj4REZGSMQnSIk87TwCQrXP0hQcX4G3vDQsjC1nKJyIiUjImQVrkZu0GI30j2TpHX3x4kf2BiIiISsAkSIv09fTRyLaRLDVBOfk5uBxzmUkQERFRCZgEaZlcw+TD4sKQnZ/NTtFEREQlYBKkZXINk7/48CL0VHpcM4yIiKgETIK0rIl9E0QlRSErL0un5V54cAE+Dj4wNzLXablERETVBZMgLfNx8IFaqHE14apOy+VM0URERKVjEqRlPg4+AKTV3HUlKy+LnaKJiIjKwCRIy2xMbFDPsh6uxF3RWZkXH1xErjoXHep30FmZRERE1Q2TIB3wreur05qgM/fOwNTAFH6Ofjork4iIqLphEqQDvg6+CIvTXRJ0+t5ptKnXBob6hjork4iIqLphEqQDzeo2w63EW8jIzdB6WUIInL53mk1hREREZWASpAO+Dr4QEIhMiNR6WXdT7uJB6gMmQURERGVgEqQDhSPEdNAkdvruaQBAB1cmQURERKVhEqQDlsaWcLN200nn6DP3zqChbUPUNa+r9bKIiIiqMyZBOuLr4IvQuFCtl3P63mm0r99e6+UQERFVd0yCdKSFUwsExwRrtYyM3AwEPQxCx/odtVoOERFRTcAkSEdaObfCg9QHiE2L1VoZZ+6dQa46F13du2qtDCIiopqCSZCOtHJuBQC4FHNJa2UcvX0UdqZ28K3rq7UyiIiIagomQTriYeMBa2NrBD0M0loZR+8cRVf3rtBT8WUlIiIqCz8tdUSlUqGlc0utJUFZeVk4c+8Murl308r5iYiIahomQTrUyqmV1pKgc/fPITs/m0kQERFROTEJ0qFWzq0QlRSFxMxEjZ/76O2jsDa25qKpRERE5cQkSIcCXAIAAOcfnNf4uQNvB6KLexfo6+lr/NxEREQ1EZMgHfKq4wU7U7vCpS00JS0nDSeiT6Bvw74aPS8REVFNprUk6PPPP0fHjh1hZmYGGxubch0jhMDs2bPh7OwMU1NT9O7dG9evX9dWiDqnp9JDh/odcPqeZpOgo7ePIledi36N+2n0vERERDWZ1pKgnJwcvPDCC5g8eXK5j1m4cCG+//57LFu2DGfPnoW5uTn69euHrKwsbYWpcx1dO+L0vdNQC7XGzrn/5n40sGkATztPjZ2TiIioptNaEvTpp59i6tSpaN68ebn2F0Lg22+/xaxZszB06FD4+flh7dq1ePDgAbZv366tMHWuQ/0OSMlOQXh8uMbOuf/mfvRt2BcqlUpj5yQiIqrpFNMnKCoqCjExMejdu3fhNmtra7Rr1w6nT5fcfJSdnY2UlJQiDyVrU68N9FX6OHX3lEbOdzvpNq49usamMCIiogpSTBIUExMDAHB0dCyy3dHRsfC54ixYsADW1taFD1dXV63GWVUWRhbwd/LHiegTGjnfvhv7oK/SRy+PXho5HxERUW1RoSToww8/hEqlKvURGRmprViLNXPmTCQnJxc+7t69q9PyK6NHgx44FHUIQogqn2vH1R3o4t4F1ibWGoiMiIio9jCoyM7vvfceXnrppVL3adiwYaUCcXJyAgDExsbC2dm5cHtsbCxatGhR4nHGxsYwNjauVJly6dOwD74+/TUiEiLg4+BT6fMkZyXj0K1DWNx3sQajIyIiqh0qlAQ5ODjAwcFBK4F4eHjAyckJhw4dKkx6UlJScPbs2QqNMKsOurh3gZG+EQ7cPFClJOjv638jV52LYd7DNBccERFRLaG1PkHR0dEIDg5GdHQ08vPzERwcjODgYKSlpRXu4+3tjW3btgGQFhh999138dlnn2Hnzp0IDQ3F+PHj4eLigmHDhmkrTFmYGZqhs1tnHLh1oErn2Ra5DQHOAXCzdtNQZERERLVHhWqCKmL27NlYs2ZN4c8tW7YEAAQGBqJ79+4AgKtXryI5Oblwn+nTpyM9PR2TJk1CUlISOnfujH379sHExERbYcqmT8M++OzYZ8jJz4GRvlGFj0/LScPf1//GzM4ztRAdERFRzacSmuidqyApKSmwtrZGcnIyrKys5A6nRJdjLqPF8hbYP3Y/+jaq+HIX6y6vw/jt43Hr7VvwsPXQQoRERETVT0XyAMUMka9t/Bz90NC2IbaEb6nU8WtD1qKre1cmQERERJXEJEgmKpUKz3k/h+1XtyNfnV+hY++l3MOhW4cw3m+8lqIjIiKq+ZgEyeh5n+cRlx6Ho3eOVui4VZdWwcTABMN9hmspMiIiopqPSZCM2tVrB087T/x26bdyH5OTn4OfL/yMcX7jOEEiERFRFTAJkpFKpcKrrV7FX+F/4XHm43Id81f4X3iY9hBvt3tby9ERERHVbEyCZDbBfwLyRT5WXVpV5r756nx8duwz9G/cH751fXUQHRERUc3FJEhmjhaOGOs3FotPL0Zmbmap+24I3YCIhAjM6z5PR9ERERHVXEyCFODjLh8jPj0eyy8uL3GflOwUzDw0E8O8h6FNvTY6jI6IiKhmYhKkAI3tGmNiy4mYc2QOHqQ+KHafD/75AMnZyfi237e6DY6IiKiGYhKkEF/1/gpmhmYY9dcoZOdlF3lu+YXlWBG0Aov7LIa7jbtMERIREdUsTIIUwtbUFltGbMG5++fQ9/e+uPTwEu6l3MOMAzPw+p7X8WabNzEpYJLcYRIREdUYWltAlSquo2tHHBp/CC9ueRGtVrQCAJgYmOCLnl/gw84fQqVSyRwhERFRzcEkSGE6uXXCjbdv4NidY0jLSUNH146oa15X7rCIiIhqHCZBCmSkb4TeDXvLHQYREVGNxj5BREREVCsxCSIiIqJaiUkQERER1UpMgoiIiKhWYhJEREREtRKTICIiIqqVmAQRERFRrcQkiIiIiGolJkFERERUKzEJIiIiolqJSRARERHVSkyCiIiIqFaqcQuoCiEAACkpKTJHQkRERLpW8PlfkA+UpsYlQampqQAAV1dXmSMhIiIiuaSmpsLa2rrUfVSiPKlSNaJWq/HgwQNYWlpCpVJp9NwpKSlwdXXF3bt3YWVlpdFzK01tudbacp1A7bnW2nKdQO25Vl5nzaPNaxVCIDU1FS4uLtDTK73XT42rCdLT00P9+vW1WoaVlVWN/wUtUFuutbZcJ1B7rrW2XCdQe66V11nzaOtay6oBKsCO0URERFQrMQkiIiKiWolJUAUYGxtjzpw5MDY2ljsUrast11pbrhOoPddaW64TqD3XyuuseZRyrTWuYzQRERFRebAmiIiIiGolJkFERERUKzEJIiIiolqJSRARERHVSkyCiIiIqFZiElQBP/74Ixo0aAATExO0a9cO586dkzskjVqwYAHatGkDS0tL1K1bF8OGDcPVq1flDksnvvzyS6hUKrz77rtyh6Jx9+/fx9ixY1GnTh2YmpqiefPmuHDhgtxhaVx+fj4++eQTeHh4wNTUFI0aNcL8+fPLtYiikh07dgxDhgyBi4sLVCoVtm/fXuR5IQRmz54NZ2dnmJqaonfv3rh+/bo8wVZRadeam5uLGTNmoHnz5jA3N4eLiwvGjx+PBw8eyBdwJZX1mj7p9ddfh0qlwrfffquz+DSpPNcaERGBZ555BtbW1jA3N0ebNm0QHR2tk/iYBJXTpk2bMG3aNMyZMwdBQUHw9/dHv379EBcXJ3doGnP06FG8+eabOHPmDA4cOIDc3Fz07dsX6enpcoemVefPn8fy5cvh5+cndygal5iYiE6dOsHQ0BB79+5FeHg4vv76a9ja2sodmsZ99dVX+Pnnn7F06VJERETgq6++wsKFC/HDDz/IHVqVpKenw9/fHz/++GOxzy9cuBDff/89li1bhrNnz8Lc3Bz9+vVDVlaWjiOtutKuNSMjA0FBQfjkk08QFBSErVu34urVq3jmmWdkiLRqynpNC2zbtg1nzpyBi4uLjiLTvLKu9ebNm+jcuTO8vb1x5MgRhISE4JNPPoGJiYluAhRULm3bthVvvvlm4c/5+fnCxcVFLFiwQMaotCsuLk4AEEePHpU7FK1JTU0Vnp6e4sCBA6Jbt27inXfekTskjZoxY4bo3Lmz3GHoxKBBg8TEiROLbHvuuefEmDFjZIpI8wCIbdu2Ff6sVquFk5OTWLRoUeG2pKQkYWxsLP744w8ZItSc/15rcc6dOycAiDt37ugmKC0o6Trv3bsn6tWrJ65cuSLc3d3FkiVLdB6bphV3rSNHjhRjx46VJyAhBGuCyiEnJwcXL15E7969C7fp6emhd+/eOH36tIyRaVdycjIAwM7OTuZItOfNN9/EoEGDiry2NcnOnTvRunVrvPDCC6hbty5atmyJX375Re6wtKJjx444dOgQrl27BgC4fPkyTpw4gQEDBsgcmfZERUUhJiamyO+vtbU12rVrV6PfmwokJydDpVLBxsZG7lA0Sq1WY9y4cfjggw/g6+srdzhao1arsWfPHnh5eaFfv36oW7cu2rVrV2rzoKYxCSqHhIQE5Ofnw9HRsch2R0dHxMTEyBSVdqnVarz77rvo1KkTmjVrJnc4WrFx40YEBQVhwYIFcoeiNbdu3cLPP/8MT09P7N+/H5MnT8bbb7+NNWvWyB2axn344YcYNWoUvL29YWhoiJYtW+Ldd9/FmDFj5A5Nawref2rTe1OBrKwszJgxAy+++GKNW3H9q6++goGBAd5++225Q9GquLg4pKWl4csvv0T//v3xzz//4Nlnn8Vzzz2Ho0eP6iQGA52UQtXOm2++iStXruDEiRNyh6IVd+/exTvvvIMDBw7oru1ZBmq1Gq1bt8YXX3wBAGjZsiWuXLmCZcuWYcKECTJHp1mbN2/G+vXrsWHDBvj6+iI4OBjvvvsuXFxcaty11na5ubkYMWIEhBD4+eef5Q5Hoy5evIjvvvsOQUFBUKlUcoejVWq1GgAwdOhQTJ06FQDQokULnDp1CsuWLUO3bt20HgNrgsrB3t4e+vr6iI2NLbI9NjYWTk5OMkWlPVOmTMHu3bsRGBiI+vXryx2OVly8eBFxcXFo1aoVDAwMYGBggKNHj+L777+HgYEB8vPz5Q5RI5ydneHj41NkW9OmTXU28kKXPvjgg8LaoObNm2PcuHGYOnVqja7pK3j/qS3vTcC/CdCdO3dw4MCBGlcLdPz4ccTFxcHNza3wvenOnTt477330KBBA7nD0yh7e3sYGBjI+h7FJKgcjIyMEBAQgEOHDhVuU6vVOHToEDp06CBjZJolhMCUKVOwbds2HD58GB4eHnKHpDW9evVCaGgogoODCx+tW7fGmDFjEBwcDH19fblD1IhOnTo9Nc3BtWvX4O7uLlNE2pORkQE9vaJvafr6+oX/bdZEHh4ecHJyKvLelJKSgrNnz9ao96YCBQnQ9evXcfDgQdSpU0fukDRu3LhxCAkJKfLe5OLigg8++AD79++XOzyNMjIyQps2bWR9j2JzWDlNmzYNEyZMQOvWrdG2bVt8++23SE9Px8svvyx3aBrz5ptvYsOGDdixYwcsLS0L+xRYW1vD1NRU5ug0y9LS8qm+Tubm5qhTp06N6gM1depUdOzYEV988QVGjBiBc+fOYcWKFVixYoXcoWnckCFD8Pnnn8PNzQ2+vr64dOkSvvnmG0ycOFHu0KokLS0NN27cKPw5KioKwcHBsLOzg5ubG95991189tln8PT0hIeHBz755BO4uLhg2LBh8gVdSaVdq7OzM4YPH46goCDs3r0b+fn5he9RdnZ2MDIykivsCivrNf1vcmdoaAgnJyc0adJE16FWWVnX+sEHH2DkyJHo2rUrevTogX379mHXrl04cuSIbgKUbVxaNfTDDz8INzc3YWRkJNq2bSvOnDkjd0gaBaDYx6pVq+QOTSdq4hB5IYTYtWuXaNasmTA2Nhbe3t5ixYoVcoekFSkpKeKdd94Rbm5uwsTERDRs2FB8/PHHIjs7W+7QqiQwMLDYv8sJEyYIIaRh8p988olwdHQUxsbGolevXuLq1avyBl1JpV1rVFRUie9RgYGBcodeIWW9pv9VnYfIl+daV65cKRo3bixMTEyEv7+/2L59u87iUwlRzadTJSIiIqoE9gkiIiKiWolJEBEREdVKTIKIiIioVmISRERERLUSkyAiIiKqlZgEERERUa3EJIiIiIhqJSZBREREVCsxCSIiIqJaiUkQERER1UpMgoiIiKhW+j9H80Qspgx2uwAAAABJRU5ErkJggg=="
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 18
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example #6: First-order DDE with one non constant delay and a constant initial history function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let the following DDE be given:\n",
    "\n",
    "$$\n",
    "y'(t)=y(t-\\mathrm{delay}(y, t))\n",
    "$$\n",
    "\n",
    "where the delay is not constant and is given by the function $\\mathrm{delay}(y, t)=|\\frac{1}{10} t y(\\frac{1}{10} t)|$, the example compares the solutions of two different cases using two different constant history functions:\n",
    "\n",
    "- Case #1: $\\phi(t)=-1$\n",
    "- Case #2: $\\phi(t)=1$"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-06T04:05:28.219142Z",
     "start_time": "2025-10-06T04:05:28.215589Z"
    }
   },
   "source": [
    "def eq(x, t, xdelay):\n",
    "    delay = abs(t * xdelay(t - 0.9 * t) / 10)  # a tensor with (1,)\n",
    "    delay = delay[0]\n",
    "    return xdelay(t - delay)"
   ],
   "outputs": [],
   "execution_count": 19
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{note}\n",
    "\n",
    "Note here we do not kwon the maximum lenght of the delay. Therefore, we can declare a fixed length delay variable with the ``delay_len`` equal to or even bigger than the running duration. \n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-06T04:05:28.370332Z",
     "start_time": "2025-10-06T04:05:28.237463Z"
    }
   },
   "source": [
    "delay1 = bm.TimeDelay(bm.ones(1), 30., before_t0=-1, dt=0.01)\n",
    "delay2 = bm.TimeDelay(-bm.ones(1), 30., before_t0=1, dt=0.01)"
   ],
   "outputs": [],
   "execution_count": 20
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-06T04:05:28.928281Z",
     "start_time": "2025-10-06T04:05:28.401371Z"
    }
   },
   "source": [
    "case1 = delay_odeint(30., eq, args={'xdelay': delay1}, state_delays={'x': delay1}, dt=0.01)\n",
    "case2 = delay_odeint(30., eq, args={'xdelay': delay2}, state_delays={'x': delay2}, dt=0.01)"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "  0%|          | 0/3000 [00:00<?, ?it/s]"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "57635299c501411687fbe0893f5bf04a"
      }
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "  0%|          | 0/3000 [00:00<?, ?it/s]"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "2d5c807abeb14c0581388736d5223976"
      }
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 21
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-06T04:05:29.118534Z",
     "start_time": "2025-10-06T04:05:28.950299Z"
    }
   },
   "source": [
    "fig, axs = plt.subplots(2, 1)\n",
    "fig.tight_layout(rect=[0, 0, 1, 0.95], pad=3.0)\n",
    "fig.suptitle(\"$y'(t)=y(t-delay(y, t))$\")\n",
    "\n",
    "axs[0].plot(case1.ts, case1.x, color='red', linewidth=1)\n",
    "axs[0].set_title('$\\phi(t)=-1$')\n",
    "\n",
    "axs[1].plot(case1.ts, case1.x, color='red', linewidth=1)\n",
    "axs[1].set_title('$\\phi(t)=1$')\n",
    "\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<>:6: SyntaxWarning: invalid escape sequence '\\p'\n",
      "<>:9: SyntaxWarning: invalid escape sequence '\\p'\n",
      "<>:6: SyntaxWarning: invalid escape sequence '\\p'\n",
      "<>:9: SyntaxWarning: invalid escape sequence '\\p'\n",
      "C:\\Users\\adadu\\AppData\\Local\\Temp\\ipykernel_57168\\4293569716.py:6: SyntaxWarning: invalid escape sequence '\\p'\n",
      "  axs[0].set_title('$\\phi(t)=-1$')\n",
      "C:\\Users\\adadu\\AppData\\Local\\Temp\\ipykernel_57168\\4293569716.py:9: SyntaxWarning: invalid escape sequence '\\p'\n",
      "  axs[1].set_title('$\\phi(t)=1$')\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ],
      "image/png": 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HjjT4eI1Gg+HDhyMqKgqff/458vPz8eabb2LkyJE4fvy4ESomMk2ZmZkoKipCz549AfwWNKoft01LS4Ofnx+cnJzQoUMHVFZWorCwEI6OjjV+z73H3evOnTuwt7dH27Zt69xeXl6O27dv61Wzu7s7rK2ta60PCAhAQkKCXr/Dy8tLr/2ISJlkCyhDhw7F0KFD691eVlaGv/3tb9iwYQPy8vIQGBiIhQsXYsCAAQCkxx2rqqrw3nvv6QbTzZw5E8OHD0dFRQVsbGxa4zSIFO/OnTsAgHbt2gEAfv75Z7i5ucHb2xs3b95ESkoKpkyZAgC6HgeNRlOrpyQ9PR1eXl5wc3Or83M0Gg0eeOCBeus4ePBgs8egeHp6YsKECXr9DiIybYodgzJ9+nScOXMGGzduhLe3NxITExEREYGTJ0+ie/fuCA4OhpWVFRISEjBhwgTcvXsX69atQ3h4OMMJ0e/cd999AIDU1FRMmTIF6enpul6QN998E1ZWVpgxYwYAICwsDABw9OjRWgElKysLnTp1qvdzjh8/rnsMuS4tMQaFiCyHIgNKVlYWEhISkJWVBW9vbwBS78iOHTuQkJCA999/H/7+/vjxxx8xevRovPLKK6iqqkJYWBi+//57masnUhZfX18MGDAA69atg4eHB37++WcEBgZi2LBh2L59O9auXat7aqdLly4IDAzErl27dINoq/n7+2P37t1YtGgRvL298cADDyA4OBiA1KN5+/ZtDB8+vN46WmIMSnMsX74ceXl5uHr1KgDg22+/xZUrVwAAr732GpycnGSrjYjqIBQAgEhMTNT9vG3bNgFAtGvXrsbSpk0bMXr0aCGEEDk5OaJ79+7i7bffFsePHxcpKSmif//+YvDgwUKr1cp0JkTKlJOTI5566ilhZ2cnAAhbW1vRt29fkZSUVGvfxYsXCwcHB1FcXFxj/a+//iqGDBkiHBwcBACxdOlS3bbo6Gjh6+ur6P/2/Pz8BIA6F41GI3d5RHQPlRDyvzxDpVLVeIpn06ZNGDduHE6fPl1roJyDgwM8PT3xj3/8Azt27MCRI0d0265cuQIfHx+kpqbisccea81TIDIJ27Ztw7Bhw3DixAk8/PDDde6Tn5+PLl26YNGiRXjxxRcb/Z1lZWXo3LkzZs2ahTfeeKOFKyYiS6XIWzyPPPIIqqqqcP36dTz++ON17lNcXFxrpsnqMKPPK+KJLFFGRgZUKhV69OhR7z5OTk545513EBcXh4kTJzY6o2tCQgJsbGx0A22JiFqCbD0od+/eRWZmJgApkCxevBgDBw6Eq6srfH19MX78eBw4cAAffvghHnnkEdy4cQNJSUno1asXnnzySezevRvh4eGYN28exo4di8LCQsyZMwcZGRk4e/ZsvY86Elmyl156Cbt27cKlS5fkLoWIqEGyBZTk5OQ6HzmMjIzEmjVrUFFRgffeew+fffYZfv31V7i5ueGxxx7D/PnzdfM5bNy4EYsWLcIvv/wCe3t7hIWFYeHChZyciagef/zjH+Hg4IAdO3bIXQoRUYMUMQaFiIiI6Pf4ulAiIiJSHIMCSmxsLEJCQuDo6IiOHTtixIgROHfunLFqIyIiIgtl0C2eiIgIPP/88wgJCUFlZSXmzJmDU6dO4cyZM7pptBuj1Wpx9epVODo68k2jREREFkYIgcLCQnh7ezf4lGCzxqDcuHEDHTt2REpKCvr166fXMdVzlRAREZHlys7ObvD1Gc2aByU/Px8A4OrqWu8+ZWVlKCsr0/1cnYeys7PRvn375nw8ERERmZiCggL4+PjUemP6vZocULRaLWbMmIG+ffsiMDCw3v1iY2Mxf/78Wuvbt2/PgEJERGShGhvm0eRbPFOnTsX27duxf//+Brto7u1BqU5O+fn5DChEREQWpqCgAE5OTo3mgCb1oEyfPh3btm3D3r17GwwnAKBWq6FWq5vyMURERGShDHrMWAiB6dOnIzExEbt379a9op2IiIjMxJdfAlOmAFVVspZhUA/KtGnTsH79emzduhWOjo7Izc0FIL1cjO++ISIiMgP/+pf09X8v4JWLQT0oK1asQH5+PgYMGAAvLy/dsmnTJmPVR0RERK1FowH27AEmTJC7EsN6UPjaHiIiIjO2di3g4ACMGiV3JXwXDxEREUEac/Lpp8DYsYCes8MbEwMKERERAT/+CGRnAy+9JHclABhQiIiICABWrwZ69gRCQuSuBAADChEREV27BnzzDTB5MqCQF/kyoBAREVm6tWulx4rHjZO7Eh0GFCIiIksmhHR759lngQZe/tvaGFCIiIgs2b59wPnzihkcW40BhYiIyJJ98gnQrRvQv7/cldTAgEJERGSp7tyR3r3z0kuKGRxbjQGFiIjIUq1ZI03QFhkpdyW1MKAQERFZIq1WejHgqFGAp6fc1dRi0Lt4iIiIyEzs3AlkZgIJCXJXUif2oBAREVmi+HigVy+gb1+5K6kTe1CIiIgszaVLwLZtwMqVihscW409KERERJZm5UqgfXtFzRx7LwYUIiIiS1JaKs0cO2EC0K6d3NXUiwGFiIjIknzxBXDrFvDqq3JX0iAGFCIiIksSHw/86U/A/ffLXUmDOEiWiIjIUqSmAocPA998I3cljWIPChERkaVYvFjqOXnySbkraRR7UIiIiCyBRgN8/bV0i8dK+f0Tyq+QiIiImu/jjwFnZ+Cvf5W7Er0woBAREZm7vDzgP/8Bpk4F7O3lrkYvDChERETmbvVqoLwcmDZN7kr0xoBCRERkzioqgKVLgRdeALy85K5GbwwoRERE5uzLL4HsbODNN+WuxCAMKEREROZKCCAuDggPl95cbEL4mDEREZG5+uEH4MQJIClJ7koMxh4UIiIic/X++0BoKDBwoNyVGIw9KEREROZo3z5p2boVUKnkrsZg7EEhIiIyR7GxQGAg8NRTclfSJOxBISIiMjcnTgDbtwOff24S09rXxTSrJiIiovrFxgJdugCjR8tdSZOxB4WIiMicZGRIc5+sXAm0Md0/8+xBISIiMicLFgD33QdERspdSbOYbrQiIiKimk6dAjZuBFasANRquatpFvagEBERmYv58wE/P2DiRLkraTb2oBAREZmDtDRp7Ml//gPY2spdTbOxB4WIiMgczJsHdO0K/OUvclfSItiDQkREZOqOHpVmjP3sM8DGRu5qWgR7UIiIiEzd3LlAjx7A2LFyV9Ji2INCRERkypKTpVljN20y6XlP7sUeFCIiIlMlBPDOO0BICPDcc3JX06LMJ2oRERFZms2bgSNHgD17TPKNxQ1hDwoREZEpKi8HZs+W3lY8YIDc1bQ49qAQERGZolWrgEuXgG++kbsSo2APChERkakpKJDeuTNxIvDQQ3JXYxQMKERERKbm/feBoiJpanszxYBCRERkSs6fBz76CJg1S3prsZliQCEiIjIlUVGAlxfw9ttyV2JUHCRLRERkKrZvB7Ztk14K2Lat3NUYFXtQiIiITEF5OTBjBjBoEDBypNzVGB17UIiIiEzB0qXAhQvAV1+Z3aRsdTG4B2Xv3r0YNmwYvL29oVKpsGXLFiOURURERDq//io9Vjx1KhAYKHc1rcLggFJUVISgoCDEx8cbox4iIiK61+uvA+3aAe++K3clrcbgWzxDhw7F0KFDjVELERER3eubb4Cvv5beVuzsLHc1rcboY1DKyspQVlam+7mgoMDYH0lERGQeCguBadOAoUPN7m3FjTH6UzyxsbFwcnLSLT4+Psb+SCIiIvMwdy5w6xbwr39ZxMDY3zN6QJk9ezby8/N1S3Z2trE/koiIyPQdOyY9uTN/PtC5s9zVtDqj3+JRq9VQq9XG/hgiIiLzUV4OTJoE9OwpzX1igTgPChERkdIsWACcOQMcOQLY2MhdjSwMDih3795FZmam7meNRoO0tDS4urrC19e3RYsjIiKyOEeOAB98AMTEAA8/LHc1slEJIYQhByQnJ2PgwIG11kdGRmLNmjWNHl9QUAAnJyfk5+ejffv2hnw0ERGReSstBXr3BuztgdRUs+w90TcHGNyDMmDAABiYaYiIiEgfc+dK09kfP26W4cQQHINCRESkBPv2AR9+CLz/PvDQQ3JXIzu+zZiIiEhut28DL7wA/PGPwMyZclejCAwoREREchICeOkloLgY+PxzwNpa7ooUgbd4iIiI5LRqFZCYKC2dOsldjWKwB4WIiEgup04Bb74JvPoqMGKE3NUoCgMKERGRHAoLgdGjgW7dgH/+U+5qFIe3eIiIiFqbENJU9leuAIcPA23byl2R4jCgEBERtbYPPwS+/BL46isgIEDuahSJt3iIiIha0549QHS0tIwcKXc1isWAQkRE1Fqys4ExY4CBA4H33pO7GkVjQCEiImoNd+8Cw4ZJ4002bADacJRFQ3h1iIiIjK2qChg7Frh4EThwAHB3l7sixWNAISIiMra33wa+/x7Ytg3o2VPuakwCAwoREZExrVoFfPQRsGwZMHSo3NWYDI5BISIiMpatW6VZYqdPlxbSGwMKERGRMaSkSE/sjBwJLFkidzUmhwGFiIiopZ04ATz9NPDHPwL//S/fUNwEDChEREQtKTMTiIgA7r9fekOxWi13RSaJAYWIiKilXLggTcLm4iI9tePoKHdFJosBhYiIqCVcuAAMGADY2wO7d3Ouk2ZiQCEiImqu6p4Te3vpXTve3nJXZPIYUIiIiJrj/HkpnNjZMZy0IAYUIiKipjp+HOjbF2jXDkhOZjhpQQwoRERETZGcLI056dwZ2LeP4aSFMaAQEREZassW6VHi0FAgKQlwc5O7IrPDgEJERKQvIaT36owaJU3Etm0bHyU2EgYUIiIifVRUAFOmAFFRwMyZwMaNnITNiPg2YyIiosbcuQM8+6w01uTTT4GJE+WuyOwxoBARETUkLU0KJ3fuADt3Av37y12RReAtHiIiovp8+ikQFiaNMzl8mOGkFTGgEBER3aukBHjxRWn5y1+AgweBrl3lrsqi8BYPERHR76WlAePHS9PXr1kDREbKXZFFYg8KERERAFRVAQsXAn36AG3aAEeOMJzIiAGFiIjo4kXpfTqzZ0uPER86BAQGyl2VRWNAISIiy1VRIfWaBAYC2dlASgrwwQec30QBGFCIiMgyHT4MPPooMGcOMHUqcPIk8PjjcldF/8OAQkREluXGDSmQPPaYNNbk8GHgww8BBwe5K6PfYUAhIiLLUFYGxMUB3bpJ09R/9JE01iQ4WO7KqA58zJiIiMybVgt8/TUQHQ1cviz1nsTE8A3ECsceFCIiMk9CAFu2AI88Ajz3HNCjB5CeDixbxnBiAhhQiIjIvGi1wLffSrdunnlGCiP79gHffw88+KDc1ZGeGFCIiMg8lJYCq1dLjww//bT0/pzkZCApCfjjH+WujgzEMShERGTabtwAVqwA4uOl759+Gli1SgolKpXc1VETMaAQEZHp0WqB3buBTz4BEhOlx4UnTABmzADuv1/u6qgFMKAQEZHpyM4G/vtf6VbOxYtAQIA0E+xf/wp06CB3ddSCGFCIiEjZrl8HvvwS2LAB2L8fsLOTnspZuxbo25e3ccwUAwoRESlPdjawbZv0mHBSkrTuiSekUDJiBNC+vZzVUStgQCEiIvlptcDRo9Ljwdu2AWlpgLW19G6c5cuBZ5/l3CUWhgGFiIhanxDA6dPSQNc9e6S3CN+5A7i4AH/+szTra0QE4Owsd6UkEwYUIiIyvuJi4Phx6d03P/0kBZIbNwBbWyAsDHjjDWDw4N9e4EcWj62AiIhaVnExcOaMNK38kSNSKElPB6qqgLZtgUcfBV5+GRg4EPjDH6R1RPdgQCEioqYpLZUe9c3IAE6e/G3JzJTGlKhUwAMPAKGhwCuvSF8DA9lDQnphKyEioroJAdy+LT1Rk5UFnD8vLZmZ0tfsbGkfQBrA2rOnNG6kVy/p+4ceAtq1k/ccyGQ1KaDEx8cjLi4Oubm5CAoKwrJly9CnT5+Wro2IiIxBCCAvT5pf5MYN6ev168CVK1Lo+P3XkpLfjmvXDujWDejeHRg37rfvu3cHPDw4Hwm1KIMDyqZNmxAVFYWVK1ciNDQUS5YswZAhQ3Du3Dl07NjRGDUSEdG9hJDGeuTlAfn5vy2//7n6+zt3pCBSHUZu3AAqK2v+PmtrwNsb8PEBOnUCHnnkt+99fABfX4YQalUqIar75/QTGhqKkJAQLF++HACg1Wrh4+OD1157DbNmzWr0+IKCAjg5OSE/Px/tOdEOESmJENJATq32t6+//76+bVVVQEUFUF4uLU35vrRU6q0oLgaKiqSvjS31/e/bygpwcvptcXEB3N2Bjh3r/+riIh1HZGT65gCDelDKy8tx7NgxzJ49W7fOysoK4eHhSE1NrfOYsrIylJWV1SjMaKZPlyb6aYg+eYz7cB/uYz771Bcy6lrXWqytpcdrbWykr9VLu3aAvf1vi4ODFB5+v656adtWmk21OoQ4O//2vYMDezrI5BkUUG7evImqqip4eHjUWO/h4YGMjIw6j4mNjcX8+fObXqEhOneW/hXSGH3+w+U+3If7mMc+VlZSINDna3P2qQ4Zvw8ddX1vY8OeCiI9GP0pntmzZyMqKkr3c0FBAXx8fIzzYTNnGuf3EhERUasyKKC4ubnB2toa165dq7H+2rVr8PT0rPMYtVoNtVrd9AqJiIjI4hjUz2hra4vg4GAkVb9ZEtIg2aSkJISFhbV4cURERGSZDL7FExUVhcjISDz66KPo06cPlixZgqKiIkycONEY9REREZEFMjigjBkzBjdu3MDcuXORm5uLhx9+GDt27Kg1cLY+1U81G/VpHiIiIlKk6r//jc1yYvA8KM115coV4w2SJSIiIpOQnZ2NTp061bu91QOKVqvF1atX4ejoCFULP6df/YRQdnY2J4EzAK9b0/C6GY7XrGl43ZqG161pjH3dhBAoLCyEt7c3rBp45L7VXxZoZWXVYGJqCe3bt2djbAJet6bhdTMcr1nT8Lo1Da9b0xjzujk5OTW6D2cLIiIiIsVhQCEiIiLFMauAolarERMTw4nhDMTr1jS8bobjNWsaXrem4XVrGqVct1YfJEtERETUGLPqQSEiIiLzwIBCREREisOAQkRERIrDgEJERESKw4BCREREimM2ASU+Ph6dO3eGnZ0dQkNDcfjwYblLUrR58+ZBpVLVWAICAuQuS3H27t2LYcOGwdvbGyqVClu2bKmxXQiBuXPnwsvLC23btkV4eDjOnz8vT7EK0th1mzBhQq32FxERIU+xChIbG4uQkBA4OjqiY8eOGDFiBM6dO1djn9LSUkybNg0dOnSAg4MDRo0ahWvXrslUsTLoc90GDBhQq81NmTJFporlt2LFCvTq1Us3W2xYWBi2b9+u266EdmYWAWXTpk2IiopCTEwMjh8/jqCgIAwZMgTXr1+XuzRFe+ihh5CTk6Nb9u/fL3dJilNUVISgoCDEx8fXuX3RokVYunQpVq5ciUOHDqFdu3YYMmQISktLW7lSZWnsugFAREREjfa3YcOGVqxQmVJSUjBt2jT89NNP2LlzJyoqKvDEE0+gqKhIt8+bb76Jb7/9Fps3b0ZKSgquXr2KkSNHyli1/PS5bgAwefLkGm1u0aJFMlUsv06dOuGDDz7AsWPHcPToUQwaNAjDhw/H6dOnASiknQkz0KdPHzFt2jTdz1VVVcLb21vExsbKWJWyxcTEiKCgILnLMCkARGJiou5nrVYrPD09RVxcnG5dXl6eUKvVYsOGDTJUqEz3XjchhIiMjBTDhw+XpR5Tcv36dQFApKSkCCGk9mVjYyM2b96s2+fs2bMCgEhNTZWrTMW597oJIUT//v3FG2+8IV9RJsDFxUWsXr1aMe3M5HtQysvLcezYMYSHh+vWWVlZITw8HKmpqTJWpnznz5+Ht7c3unTpgnHjxiErK0vukkyKRqNBbm5ujbbn5OSE0NBQtj09JCcno2PHjujRowemTp2KW7duyV2S4uTn5wMAXF1dAQDHjh1DRUVFjTYXEBAAX19ftrnfufe6Vfv888/h5uaGwMBAzJ49G8XFxXKUpzhVVVXYuHEjioqKEBYWpph21upvM25pN2/eRFVVFTw8PGqs9/DwQEZGhkxVKV9oaCjWrFmDHj16ICcnB/Pnz8fjjz+OU6dOwdHRUe7yTEJubi4A1Nn2qrdR3SIiIjBy5Ej4+/vjwoULmDNnDoYOHYrU1FRYW1vLXZ4iaLVazJgxA3379kVgYCAAqc3Z2trC2dm5xr5sc7+p67oBwAsvvAA/Pz94e3sjPT0d0dHROHfuHL7++msZq5XXyZMnERYWhtLSUjg4OCAxMREPPvgg0tLSFNHOTD6gUNMMHTpU932vXr0QGhoKPz8/fPHFF3jxxRdlrIwswfPPP6/7vmfPnujVqxe6du2K5ORkDB48WMbKlGPatGk4deoUx4YZqL7r9vLLL+u+79mzJ7y8vDB48GBcuHABXbt2be0yFaFHjx5IS0tDfn4+vvzyS0RGRiIlJUXusnRM/haPm5sbrK2ta40uvnbtGjw9PWWqyvQ4Ozvj/vvvR2ZmptylmIzq9sW213xdunSBm5sb29//TJ8+Hdu2bcOePXvQqVMn3XpPT0+Ul5cjLy+vxv5sc5L6rltdQkNDAcCi25ytrS26deuG4OBgxMbGIigoCB9//LFi2pnJBxRbW1sEBwcjKSlJt06r1SIpKQlhYWEyVmZa7t69iwsXLsDLy0vuUkyGv78/PD09a7S9goICHDp0iG3PQFeuXMGtW7csvv0JITB9+nQkJiZi9+7d8Pf3r7E9ODgYNjY2NdrcuXPnkJWVZdFtrrHrVpe0tDQAsPg293tarRZlZWXKaWetNhzXiDZu3CjUarVYs2aNOHPmjHj55ZeFs7OzyM3Nlbs0xXrrrbdEcnKy0Gg04sCBAyI8PFy4ubmJ69evy12aohQWFooTJ06IEydOCABi8eLF4sSJE+Ly5ctCCCE++OAD4ezsLLZu3SrS09PF8OHDhb+/vygpKZG5cnk1dN0KCwvFzJkzRWpqqtBoNGLXrl2id+/eonv37qK0tFTu0mU1depU4eTkJJKTk0VOTo5uKS4u1u0zZcoU4evrK3bv3i2OHj0qwsLCRFhYmIxVy6+x65aZmSkWLFggjh49KjQajdi6davo0qWL6Nevn8yVy2fWrFkiJSVFaDQakZ6eLmbNmiVUKpX48ccfhRDKaGdmEVCEEGLZsmXC19dX2Nraij59+oiffvpJ7pIUbcyYMcLLy0vY2tqK++67T4wZM0ZkZmbKXZbi7NmzRwCotURGRgohpEeN//GPfwgPDw+hVqvF4MGDxblz5+QtWgEaum7FxcXiiSeeEO7u7sLGxkb4+fmJyZMn8x8UQtR5zQCIhIQE3T4lJSXi1VdfFS4uLsLe3l4888wzIicnR76iFaCx65aVlSX69esnXF1dhVqtFt26dRNvv/22yM/Pl7dwGU2aNEn4+fkJW1tb4e7uLgYPHqwLJ0Ioo52phBCi9fpriIiIiBpn8mNQiIiIyPwwoBAREZHiMKAQERGR4jCgEBERkeIwoBAREZHiMKAQERGR4jCgEBERkeIwoBAREZHiMKAQERGR4jCgEBERkeIwoBAREZHiMKAQERGR4jCgEBERkeIwoBAREZHiMKAQERGR4jCgEBERkeIwoBAREZHiMKAQERGR4jCgEBERkeIwoBAREZHiMKAQERGR4jCgEBERkeIwoBAREZHiMKAQERGR4jCgEBERkeIwoBAREZHiMKAQUS3BwcF45pln6ty2aNEiBAQEQKvVNvp7Vq5cCV9fX5SVlbV0iURk5hhQiKgGIQQyMjLw4IMP1tpWUFCAhQsXIjo6GlZWVrWOW7BgAfbt26dbN2HCBJSXl2PVqlVGr/vu3buIiYlBREQEXF1doVKpsGbNGqN/LhEZBwMKEdVw6dIlFBcX1xlQPv30U1RWVmLs2LG1tv3yyy+IiYlBTk6Obp2dnR0iIyOxePFiCCGMWvfNmzexYMECnD17FkFBQUb9LCIyPgYUIqrhzJkzAFBnQElISMDTTz8NOzu7WtuOHTsGAOjdu3eN9aNHj8bly5exZ88eI1T7Gy8vL+Tk5ODy5cuIi4sz6mcRkfExoBARACAxMbHG2JPHH38c48aNQ35+PgBAo9EgPT0d4eHhtY7t06cPxo0bBwDo3r07VCoVnJ2dAUjjWVxdXbF161aj1q9Wq+Hp6WnUzyCi1tNG7gKISH5xcXF45513MHbsWFRUVKCgoAARERFYtWoVhBBYv349Dh48CKB2DwkAREdHY968eSgrK8PcuXMBQBdQqo85cOBAvZ9fUVGhC0KNcXV1rTX+hYjMDwMKkYU7cuQIoqOjMXPmTMTFxaFHjx74wx/+gJUrV+LixYvYvHkzVq9ejYyMDACAv79/rd8xatQoREVFYdCgQRg/fnyt7V26dMG6devqreHAgQMYOHCgXvVqNBp07txZv5MjIpPFgEJk4RYuXAh3d3csWLAAJSUlyMzMxKRJkwAAffv2xc6dO3H9+nXcunULbdq0gYODQ63fkZ+fj6ysLPTq1avOz3BxcUFJSQmKi4thb29fa3tQUBB27typV728jUNkGRhQiCxYZWUlduzYgWeffRZt27bFkSNHoNVqdUGjqKgIgBQwGpKeng4A9QaU6id4VCpVndtdXFzqHNtCRJZLthu5e/fuxbBhw+Dt7Q2VSoUtW7YY/Dt++OEHPPbYY3B0dIS7uztGjRqFS5cutXitROYqMzMTRUVF6NmzJ4Dfgkb1Y7ppaWnw8/ODk5MTOnTogMrKShQWFtb6Pfced687d+7A3t4ebdu2rXN7eXk5cnNz9Vqqqqqafd5EpHyyBZSioiIEBQUhPj6+ScdrNBoMHz4cgwYNQlpaGn744QfcvHkTI0eObOFKiczXnTt3AADt2rUDAPz8889wc3ODt7c3bt68iZSUFAwfPhwAEBAQAED6b+9e6enp8PLygpubW52fo9Fo8MADD9Rbx8GDB+Hl5aXXkp2d3axzJiLTINstnqFDh2Lo0KH1bi8rK8Pf/vY3bNiwAXl5eQgMDMTChQsxYMAAANKcC1VVVXjvvfd0I/pnzpyJ4cOHo6KiAjY2Nq1xGkQm7b777gMApKamYsqUKUhPT9f1grz55puwsrLCjBkzAABhYWEAgKNHj9a6lZOVlYVOnTrV+znHjx/XPYZcF45BIaJ7KXYMyvTp03HmzBls3LgR3t7eSExMREREBE6ePInu3bsjODgYVlZWSEhIwIQJE3D37l2sW7cO4eHhDCdEevL19cWAAQOwbt06eHh44Oeff0ZgYCCGDRuG7du3Y+3atbqndrp06YLAwEDs2rVLN4i2mr+/P3bv3o1FixbB29sbDzzwAIKDgwFI/5i4ffu2riemLi01BmX58uXIy8vD1atXAQDffvstrly5AgB47bXX4OTk1OzPIKJWIhQAgEhMTNT9fPnyZWFtbS1+/fXXGvsNHjxYzJ49W/dzcnKy6Nixo7C2thYARFhYmLhz504rVU1kHnJycsRTTz0l7OzsBABha2sr+vbtK5KSkmrtu3jxYuHg4CCKi4trrP/111/FkCFDhIODgwAgli5dqtsWHR0tfH19hVarNfq5+Pn5CQB1LhqNxuifT0QtR5GzHZ08eRJVVVW4//774eDgoFtSUlJw4cIFAEBubi4mT56MyMhIHDlyBCkpKbC1tcWzzz5r9Hd+EJkTT09PfPvtt9i8eTMA4NChQ9i/fz8GDRpUa99JkybB1tYW69evr7He29sbO3bsQGFhIYQQeO211wBIt2rXrl2LqKioep/gaUmXLl2CEKLOhXOnEJkWRd7iuXv3LqytrXHs2DFYW1vX2FY9B0N8fDycnJywaNEi3bb//ve/8PHxwaFDh/DYY4+1as1Epi4jIwMqlQo9evSodx8nJye88847iIuLw8SJExud0TUhIQE2NjaYMmVKS5dLRGZOkT0ojzzyCKqqqnD9+nV069atxlI9QK64uLjW/xyrw4xWq231molMXUZGBnx9fet9FLhadHQ0MjIy9JpufsqUKcjKyoJarW6pMonIQsgWUO7evYu0tDSkpaUBkB5DTEtLQ1ZWFu6//36MGzcOf/3rX/H1119Do9Hg8OHDiI2NxXfffQcAePLJJ3HkyBEsWLAA58+fx/HjxzFx4kT4+fnhkUcekeu0iExWRkaG7lFiIiK5qYRMAzaSk5PrfPdGZGQk1qxZg4qKCrz33nv47LPP8Ouvv8LNzQ2PPfYY5s+fr5tUauPGjVi0aBF++eUX2NvbIywsDAsXLuT/ZImIiEycbAGFiIiIqD4G3eKJjY1FSEgIHB0d0bFjR4wYMQLnzp0zVm1ERERkoQzqQYmIiMDzzz+PkJAQVFZWYs6cOTh16hTOnDmjmyq7MVqtFlevXoWjo2OrPHZIREREyiGEQGFhIby9vRscbN+sWzw3btxAx44dkZKSgn79+ul1zJUrV+Dj49PUjyQiIiIzkJ2d3eArMpo1D0p+fj4AwNXVtd59ysrKUFZWpvu5Og9lZ2ejffv2zfl4IiIiMjEFBQXw8fGBo6Njg/s1OaBotVrMmDEDffv2RWBgYL37xcbGYv78+bXWt2/fngGFiIjIQjU2zKPJt3imTp2K7du3Y//+/Q120dzbg1KdnPLz8xlQiIiILExBQQGcnJwazQFN6kGZPn06tm3bhr179zYYTgBArVZzFkkiIiIyiEGPGQshMH36dCQmJmL37t2617ATERGRmdi7F1i6FKiqkrUMgwLKtGnT8N///hfr16+Ho6MjcnNzkZubi5KSEmPVR0RERK1pyRJgzRrgnpf1tjaDAsqKFSuQn5+PAQMGwMvLS7ds2rTJWPURERFRa7lxA/j2W2DCBLkrMWwMCmfFJyIiMmPr1wMqFfDCC3JXIt/bjImIiEhBhAA++QQYPhxwc5O7GgYUIiIiAnDoEHD6NDB5styVAGBAISIiIgBYvRrw8wPCw+WuBAADChERERUWAhs3ApMmAQ28wK81KaMKIiIiks/GjUBJCTBxotyV6DCgEBERWbrVq4GICMDHR+5KdJr1NmMiIiIycenpwOHDwNdfy11JDexBISIismSrVwMeHsBTT8ldSQ0MKERERJaqpARYt06aOdbGRu5qamBAISIislRffAHk5QEvvih3JbUwoBAREVmq+HjgiSeA7t3lrqQWDpIlIiKyREeOSMvWrXJXUif2oBAREVmi+Hhp5tgnn5S7kjoxoBAREVmamzelydmmTAGsreWupk4MKERERJbm00+ltxcrcHBsNQYUIiIiS1JVBaxYAYwZA7i7y11NvThIloiIyJJs3w5cuiTd4lEw9qAQERFZkvh4IDgY6NNH7koaxB4UIiIiS5GRAezYASQkACqV3NU0iD0oRERElmLJEum9O2PHyl1JoxhQiIiILMHNm8DatcD06YBaLXc1jWJAISIisgQrVki3daZMkbsSvTCgEBERmbvSUmD5ciAyEnBzk7savTCgEBERmbsNG4Dr14EZM+SuRG8MKEREROZMCGDxYuCpp4AePeSuRm98zJiIiMic7doFnDoFLFsmdyUGYQ8KERGROYuLAx55BOjfX+5KDMIeFCIiInN19Ciwc6c0rb3CJ2a7F3tQiIiIzFVsLNC9O/Dss3JXYjD2oBAREZmjM2eAr78G/vMfwNpa7moMxh4UIiIic7RwIdCpEzB+vNyVNAl7UIiIiMzNpUvA559Ljxfb2spdTZOwB4WIiMjcxMUBLi7ASy/JXUmTMaAQERGZk5wcadzJm28C9vZyV9NkDChERETmZOFCwM4OePVVuStpFgYUIiIic3HlCrByJfDWW4Czs9zVNAsDChERkbmIjQXatQPeeEPuSpqNAYWIiMgcXL4MfPIJ8PbbQPv2clfTbAwoRERE5uD//k+6rTN9utyVtAgGFCIiIlN38SKQkABERwMODnJX0yIYUIiIiEzdu+8Cbm7A1KlyV9JiOJMsERGRKTt1CvjsM2DJEpOe9+Re7EEhIiIyZbNmAf7+wCuvyF1Ji2IPChERkalKTga++w7YtMlk37lTH/agEBERmSIhgHfeAUJCgOeek7uaFsceFCIiIlO0eTNw5AiwZw+gUsldTYtjDwoREZGpKS8H5swBnnwSGDBA7mqMgj0oREREpmbFCkCjAbZskbsSo2EPChERkSm5cQOIiQEmTwYCA+WuxmgYUIiIiEzJ3/4mjTl57z25KzEq3uIhIiIyFceOAatXA0uXSjPHmjH2oBAREZkCIYDXXwceegiYMkXuaoyOPShERESmYP164OBBICkJaGP+f74N7kHZu3cvhg0bBm9vb6hUKmwx4xHEREREilBQIE3K9uyzwKBBclfTKgwOKEVFRQgKCkJ8fLwx6iEiIqJ7/f3vQH4+8OGHclfSagzuIxo6dCiGDh1qjFqIiIjoXocPA8uXS+HE11fualqN0W9ilZWVoaysTPdzQUGBsT+SiIjIPFRWAi+/DDzyCPDaa3JX06qM/hRPbGwsnJycdIuPj4+xP5KIiMg8LFkCnDwJ/PvfFjEw9veMHlBmz56N/Px83ZKdnW3sjyQiIjJ9ly5JM8a+9hoQHCx3Na3O6HFMrVZDrVYb+2OIiIjMhxDAK68Arq7Au+/KXY0sLKu/iIiIyBT8+9/Ajz8C27cDjo5yVyMLgwPK3bt3kZmZqftZo9EgLS0Nrq6u8LWg0cVERERGodEAb70lvQwwIkLuamSjEkIIQw5ITk7GwIEDa62PjIzEmjVrGj2+oKAATk5OyM/PR/v27Q35aCIiIvOm1QKDBwMXL0qDY83w76S+OcDgHpQBAwbAwExDRERE+oiPB5KTpenszTCcGIIvCyQiIlKCc+eA6Ghg2jSLmc6+IQwoREREcisrA55/XpopduFCuatRBD7FQ0REJLdZs4AzZ4CffgLatZO7GkVgQCEiIpLTd99JM8YuWSJNaU8AeIuHiIhIPlevAhMmAE8+Cbz+utzVKAoDChERkRwqK4Hx4wEbGyAhAVCp5K5IUXiLh4iISA5z5gB79wK7dgHu7nJXozgMKERERK3tyy+BuDjgn/8EBgyQuxpF4i0eIiKi1nT2LDBxIjB6NBAVJXc1isWAQkRE1FoKC4GRI6X5Tv7zH447aQBv8RAREbWGykppMrarV4HDhwEHB7krUjQGFCIiotbw1lvADz9I85706CF3NYrHgEJERGRs//oXsHSp9DLAIUPkrsYkcAwKERGRMf3wgzQJ2+uvA6++Knc1JoMBhYiIyFiOHweee07qNVm8WO5qTAoDChERkTH88gsQEQEEBACbNgHW1nJXZFIYUIiIiFrar78CTzwBdOgAfP89n9hpAgYUIiKilnT7tnRLR6sFfvwRcHOTuyKTxKd4iIiIWkpenhROcnOB/fsBHx+5KzJZDChEREQtIS8P+NOfgIsXpRcABgTIXZFJ4y0eIiKi5srLk8acVIeTRx6RuyKTx4BCRETUHHfuSOHkwgWGkxbEgEJERNRUV68C/fqx58QIOAaFiIioKc6fl3pOKiuBffuABx6QuyKzwh4UIiIiQ504Afzxj4BaDRw4wHBiBAwoREREhti+HejfH/Dzkx4l9vWVuyKzxIBCRESkDyGAjz8GnnoKGDAASEriJGxGxIBCRETUmIoK6U3EM2YAUVFAYiLg6Ch3VWaNg2SJiIgacu0aMHasNBB29WrgxRflrsgiMKAQERHVZ/9+YPRo6b06u3ZJY0+oVfAWDxER0b2EAD78UBpr0r279NQOw0mrYkAhIiL6vevXgeHDgZkzgbfekgbDennJXZXF4S0eIiKiat98A7z00m/fDxsmbz0WjD0oREREhYXA5MlSz0loKHDyJMOJzNiDQkRElu3bb4Fp04Dbt4F//1vqQVGp5K7K4rEHhYiILFNODvDcc8DTTwMPPgikp0u9KAwnisCAQkRElqWiAli2THp/TkoKsH69NH19ly5yV0a/w4BCRESWQQjg+++BXr2AN96Q5jfJyJAmYWOvieIwoBARkfk7eRKIiACefBLw9ASOH5fGm7i6yl0Z1YMBhYiIzNfZs8DzzwNBQcCFC9I7dHbvBh5+WO7KqBEMKEREZH5++QUYPx546CHg4EFg5UrgzBlgxAjezjERfMyYiIjMR2qqNEV9YqI0+2t8PDBpEqBWy10ZGYg9KEREZNqqqoCvvgL+8AdpOXlSCiaZmcDUqQwnJoo9KEREZJquXAE+/RT4z3+ArCygXz9g61bgqacAK/7729QxoBARkemoqJDmLPnkE+mR4bZtpceEX3kFePRRuaujFsSAQkREyqbVAvv2ARs2AF9+Cdy6JYWRFSukcOLoKHeFZAQMKEREpDyVldLTN1u2AJs2AVevAn5+0ntyxo6VHhsms8aAQkREynDnDrBjB7Btm3Qb584daVK1556TQsljj/ERYQvCgEJERPIoKZF6SXbvBvbsAQ4flp7IefhhYPp0YNgwIDiYA14tFAMKERG1jtu3pRDy009AcrI0Z0l5OeDuDgwYAERGSlPRd+okd6WkAAwoRETU8oqKpPlIjhwBDh2Sgsn589I2V1fpkeC4OGDQIODBB9lLQrUwoBARUdNVVkrvuDl58rclPR24eFF6e7CtrXTLJiICiIkBQkOBrl05loQaxYBCREQNKysDsrOlHpDMzJpfL12SQgoAeHgAPXsCTz8N9OolfR8YyJlcqUmaFFDi4+MRFxeH3NxcBAUFYdmyZejTp09L10ZERMYkhPSkzI0bwPXr0sys2dm/LdU/X7/+2zG2tlIPSPfuUhDp3l1aevYEOnaU71zI7BgcUDZt2oSoqCisXLkSoaGhWLJkCYYMGYJz586hIxsnEVHr02qBwkIgP19a8vJqfl8dQqqDSPXXmzd/6/2o5uQkDVL18QF695ZCiI8P4OsLdOsmbbO2luMsycKohBDCkANCQ0MREhKC5cuXAwC0Wi18fHzw2muvYdasWY0eX1BQACcnJ+Tn56N9+/ZNq5qISGmEkB6RLS+XloqK376/9+e6vi8tlR67LS7WfykslAJIQYH0+XVp0wZwcZGelOnYseGvnTpxVlYyOn1zgEE9KOXl5Th27Bhmz56tW2dlZYXw8HCkpqbWeUxZWRnKyspqFGY0//wncPZsw/vok8e4D/fhPuazj1YrLVVVNb82Z92926qDSUuwt294cXaWvrZtC7RvL/V4ODlJ6+v6vm1bDkglk2RQQLl58yaqqqrg4eFRY72HhwcyMjLqPCY2Nhbz589veoWGuHy58YAC6Pcfq77/QbfU7+Ln8fOM9XmN7Wvq59cYKyvploQ+X5uzj62ttNjY1P6+rnX3fm9ryzBB9DtGf4pn9uzZiIqK0v1cUFAAHx8f43zYsmXG+b1ERETUqgwKKG5ubrC2tsa1a9dqrL927Ro8PT3rPEatVkPNR8yIiIjIAAZN3Wdra4vg4GAkJSXp1mm1WiQlJSEsLKzFiyMiIiLLZPAtnqioKERGRuLRRx9Fnz59sGTJEhQVFWHixInGqI+IiIgskMEBZcyYMbhx4wbmzp2L3NxcPPzww9ixY0etgbP1qX6q2ahP8xAREZEiVf/9b2yWE4PnQWmuK1euGG+QLBEREZmE7OxsdGrgzdWtHlC0Wi2uXr0KR0dHqFr4cbrqJ4Sys7M5CZwBeN2ahtfNcLxmTcPr1jS8bk1j7OsmhEBhYSG8vb1h1cBbrFv9ZYFWVlYNJqaW0L59ezbGJuB1axpeN8PxmjUNr1vT8Lo1jTGvm5OTU6P7GPQUDxEREVFrYEAhIiIixTGrgKJWqxETE8OJ4QzE69Y0vG6G4zVrGl63puF1axqlXLdWHyRLRERE1Biz6kEhIiIi88CAQkRERIrDgEJERESKw4BCREREisOAQkRERIpjNgElPj4enTt3hp2dHUJDQ3H48GG5S1K0efPmQaVS1VgCAgLkLktx9u7di2HDhsHb2xsqlQpbtmypsV0Igblz58LLywtt27ZFeHg4zp8/L0+xCtLYdZswYUKt9hcRESFPsQoSGxuLkJAQODo6omPHjhgxYgTOnTtXY5/S0lJMmzYNHTp0gIODA0aNGoVr167JVLEy6HPdBgwYUKvNTZkyRaaK5bdixQr06tVLN1tsWFgYtm/frtuuhHZmFgFl06ZNiIqKQkxMDI4fP46goCAMGTIE169fl7s0RXvooYeQk5OjW/bv3y93SYpTVFSEoKAgxMfH17l90aJFWLp0KVauXIlDhw6hXbt2GDJkCEpLS1u5UmVp7LoBQERERI32t2HDhlasUJlSUlIwbdo0/PTTT9i5cycqKirwxBNPoKioSLfPm2++iW+//RabN29GSkoKrl69ipEjR8pYtfz0uW4AMHny5BptbtGiRTJVLL9OnTrhgw8+wLFjx3D06FEMGjQIw4cPx+nTpwEopJ0JM9CnTx8xbdo03c9VVVXC29tbxMbGyliVssXExIigoCC5yzApAERiYqLuZ61WKzw9PUVcXJxuXV5enlCr1WLDhg0yVKhM9143IYSIjIwUw4cPl6UeU3L9+nUBQKSkpAghpPZlY2MjNm/erNvn7NmzAoBITU2Vq0zFufe6CSFE//79xRtvvCFfUSbAxcVFrF69WjHtzOR7UMrLy3Hs2DGEh4fr1llZWSE8PBypqakyVqZ858+fh7e3N7p06YJx48YhKytL7pJMikajQW5ubo225+TkhNDQULY9PSQnJ6Njx47o0aMHpk6dilu3bsldkuLk5+cDAFxdXQEAx44dQ0VFRY02FxAQAF9fX7a537n3ulX7/PPP4ebmhsDAQMyePRvFxcVylKc4VVVV2LhxI4qKihAWFqaYdtbqbzNuaTdv3kRVVRU8PDxqrPfw8EBGRoZMVSlfaGgo1qxZgx49eiAnJwfz58/H448/jlOnTsHR0VHu8kxCbm4uANTZ9qq3Ud0iIiIwcuRI+Pv748KFC5gzZw6GDh2K1NRUWFtby12eImi1WsyYMQN9+/ZFYGAgAKnN2drawtnZuca+bHO/qeu6AcALL7wAPz8/eHt7Iz09HdHR0Th37hy+/vprGauV18mTJxEWFobS0lI4ODggMTERDz74INLS0hTRzkw+oFDTDB06VPd9r169EBoaCj8/P3zxxRd48cUXZayMLMHzzz+v+75nz57o1asXunbtiuTkZAwePFjGypRj2rRpOHXqFMeGGai+6/byyy/rvu/Zsye8vLwwePBgXLhwAV27dm3tMhWhR48eSEtLQ35+Pr788ktERkYiJSVF7rJ0TP4Wj5ubG6ytrWuNLr527Ro8PT1lqsr0ODs74/7770dmZqbcpZiM6vbFttd8Xbp0gZubG9vf/0yfPh3btm3Dnj170KlTJ916T09PlJeXIy8vr8b+bHOS+q5bXUJDQwHAotucra0tunXrhuDgYMTGxiIoKAgff/yxYtqZyQcUW1tbBAcHIykpSbdOq9UiKSkJYWFhMlZmWu7evYsLFy7Ay8tL7lJMhr+/Pzw9PWu0vYKCAhw6dIhtz0BXrlzBrVu3LL79CSEwffp0JCYmYvfu3fD396+xPTg4GDY2NjXa3Llz55CVlWXRba6x61aXtLQ0ALD4Nvd7Wq0WZWVlymlnrTYc14g2btwo1Gq1WLNmjThz5ox4+eWXhbOzs8jNzZW7NMV66623RHJystBoNOLAgQMiPDxcuLm5ievXr8tdmqIUFhaKEydOiBMnTggAYvHixeLEiRPi8uXLQgghPvjgA+Hs7Cy2bt0q0tPTxfDhw4W/v78oKSmRuXJ5NXTdCgsLxcyZM0VqaqrQaDRi165donfv3qJ79+6itLRU7tJlNXXqVOHk5CSSk5NFTk6ObikuLtbtM2XKFOHr6yt2794tjh49KsLCwkRYWJiMVcuvseuWmZkpFixYII4ePSo0Go3YunWr6NKli+jXr5/Mlctn1qxZIiUlRWg0GpGeni5mzZolVCqV+PHHH4UQymhnZhFQhBBi2bJlwtfXV9ja2oo+ffqIn376Se6SFG3MmDHCy8tL2Nraivvuu0+MGTNGZGZmyl2W4uzZs0cAqLVERkYKIaRHjf/xj38IDw8PoVarxeDBg8W5c+fkLVoBGrpuxcXF4oknnhDu7u7CxsZG+Pn5icmTJ/MfFELUec0AiISEBN0+JSUl4tVXXxUuLi7C3t5ePPPMMyInJ0e+ohWgseuWlZUl+vXrJ1xdXYVarRbdunUTb7/9tsjPz5e3cBlNmjRJ+Pn5CVtbW+Hu7i4GDx6sCydCKKOdqYQQovX6a4iIiIgaZ/JjUIiIiMj8MKAQERGR4jCgEBERkeIwoBAREZHiMKAQERGR4jCgEBERkeIwoBAREZHiMKAQERGR4jCgEBERkeIwoBAREZHiMKAQERGR4vw/Lgq/r6SOmYcAAAAASUVORK5CYII="
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 22
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "## Delay SDEs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Save as delay ODEs, state-dependent delay variables can be appended into ``state_delay`` argument in ``brainpy.sdeint`` function."
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2025-10-06T04:05:29.163348Z",
     "start_time": "2025-10-06T04:05:29.147480Z"
    }
   },
   "source": [
    "delay = bm.TimeDelay(bm.zeros(1),\n",
    "                     2.,\n",
    "                     before_t0=lambda t: bm.exp(-t) - 1,\n",
    "                     dt=0.01,\n",
    "                     interp_method='round')\n",
    "\n",
    "f = lambda x, t: -delay(t - 2)\n",
    "g = lambda x, t, *args: 0.01\n",
    "\n",
    "dt = 0.01\n",
    "integral = bp.sdeint(f, g, state_delays={'x': delay})"
   ],
   "outputs": [],
   "execution_count": 23
  },
  {
   "cell_type": "code",
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2025-10-06T04:05:29.863517Z",
     "start_time": "2025-10-06T04:05:29.188906Z"
    }
   },
   "source": [
    "runner = bp.IntegratorRunner(integral,\n",
    "                             monitors=['x'],\n",
    "                             dt=dt)\n",
    "runner.run(100.)\n",
    "\n",
    "plt.plot(runner.mon.ts, runner.mon.x)\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "  0%|          | 0/10000 [00:00<?, ?it/s]"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "b6f857374feb41a184aff1b950b16837"
      }
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 24
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "## Delay FDEs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    " Fractional order delayed differential equations as the generalization of the delayed differential equations, provide more freedom when we're describing these systems, let's see how we can use BrainPy to accelerate the simulation of fractional order delayed differential equations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "The fractional delayed differential equations has the general form:\n",
    "\n",
    "$$\n",
    "\\begin{gathered}\n",
    "D_{t}^{\\alpha} y(t)=f(t, y(t), y(t-\\tau)), \\quad t \\geq \\xi \\\\\n",
    "y(t)=\\phi(t), \\quad t \\in[\\xi-\\tau, \\xi]\n",
    "\\end{gathered}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "#### Lemmings’ population cycle\n",
    "\n",
    "The fractional order version of the four-year life cycle of a population of lemmings is given by\n",
    "\n",
    "\\begin{split}\n",
    "\\begin{gathered}\n",
    "D_{t}^{\\alpha} y(t)=3.5 y(t)\\left(1-\\frac{y(t-0.74)}{19}\\right), \\\\\n",
    " y(0)=19.00001 \\\\\n",
    "y(t)=19, t<0\n",
    "\\end{gathered}\n",
    "\\end{split}\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2025-10-06T04:05:30.345660Z",
     "start_time": "2025-10-06T04:05:29.873484Z"
    }
   },
   "source": [
    "dt = 0.05\n",
    "delay = bm.TimeDelay(bm.asarray([19.00001]), 0.74, before_t0=19., dt=dt)\n",
    "f = lambda y, t: 3.5 * y * (1 - delay(t - 0.74) / 19)\n",
    "integral = bp.fde.GLShortMemory(f,\n",
    "                                alpha=0.97,\n",
    "                                inits=[19.00001],\n",
    "                                num_memory=500,\n",
    "                                state_delays={'y': delay})"
   ],
   "outputs": [],
   "execution_count": 25
  },
  {
   "cell_type": "code",
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2025-10-06T04:05:31.017776Z",
     "start_time": "2025-10-06T04:05:30.350149Z"
    }
   },
   "source": [
    "_mon_f = lambda s: delay(s['t'] - 0.74)\n",
    "\n",
    "runner = bp.IntegratorRunner(integral,\n",
    "                             inits=bm.asarray([19.00001]),\n",
    "                             monitors={'y(t-0.74)': _mon_f, 'y': 'y'},\n",
    "                             dt=dt)\n",
    "runner.run(100.)\n",
    "\n",
    "plt.plot(runner.mon['y'], runner.mon['y(t-0.74)'])\n",
    "plt.xlabel('y(t)')\n",
    "plt.ylabel('y(t-0.74)')\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "  0%|          | 0/2000 [00:00<?, ?it/s]"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "e701464cb9c541d092e85bfea8d0355d"
      }
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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REVkrhh0bcUNPH9wWHQShaSmJRm37lpK4WIinM5Jfv/mS7edLajkPDxER2R2GHRvyr1v6wtNFhrSiany979x1nUvh5ID0t6e0uo+Bh4iI7AnDjg3xdJHh1VsMS0ks33UWB8+WXtf5ZFJxqyulAww8RERkPxh2bMysgUGYNiAAjTo9Hv7xKBKzr73/DmAYmp61bFqr+xh4iIjIHjDs2BiRSISP7orC2B7eqGvUYf6KIzhVUHXd571S4LmWtbmIiIisBcOODZJLJfjf/YMxJKwLqhq0eOD7eJwvqbnu82YtmwYHieiS7RFLtqC0pv3LVRAREVkDhh0b5SyT4rt5Q9E3wB2lNY2479t45FfWX/d5M96ZiiAPp0u2D3l753V3iiYiIrIEhh0bpnBywI8LhqGrjwsKVA2479v4a1ow9J8OLp6A/5vc+5Lt7245w348RERkcxh2bJy3qxyrHhqOIA8nZJbW4v7v4qGq01z3eR8f3w37Xrx08kGAHZeJiMi2MOzYgQCFE1Y9NBw+bnKcUVZj3sojqL3GNbQuFurljHPvXn5ouk7PjstERGT9GHbsRLi3C35aMAwKJwccy6nEIz8dRYNGd93nlYgvPzS928tbsDW18Lpfg4iIyJQYduxIb393/PDgMLjIJDh4tgwL1xyDRnfty0pcLGvZNDw8NuKS7Y+vSuJtLSIismoMO3ZmYIgHvp07FDKpGDtOFeGl31Kg76DbTa9M64sV84e2uo+Bh4iIrBXDjh0a2c0LX947CFKxCOuP5eO1jSc6bGLAG3v54tirN7W6L3xxLE4XXv8Eh0RERB2JYcdOTezjh4/uGgiRCPj5cA7e357WYefu4iLDmbcmt7pvyqf72cpDRERWhWHHjs2ICsQ7swYAAL7ccw5f7DnbYed2dJDg/LtT0d3XtdX9XGaCiIisBcOOnbtneChenmqYIPD9bWn4KS6rw84tFouw87lxeP6mnq3uj1iyBT8c6rjXIyIiuhYMO53AIzd0w8IJ3QEAr/55EuuP5XXo+RdO7HHZjsuvbzzJ21pERGRRDDudxHM39cS8UeEAgBfWpWD7SWWHnv/GXr6IfXrMZfeHL47tkMVKiYiI2othp5MQiUR47Za+uH1wMHR6AQtXH8OBjNIOfY1+gQrELZmAPgHure6f8OFetvIQEZHZMex0ImKxCMtuG4Ap/f3RqNPj4R+P4u+04g59jQCFEzY8OarVhUSbhS+ORXF1Q4e+LhER0eUw7HQyUokYn8wZiBt6+qBeo8P8FQl4b9sZaDtopmUAkEsleHx8NxxeMhHTowJbPWbYO7vYykNERGbBsNMJyaUSfH3/YNw/IgyAYVj63d8cRqGqvkNfx1/hiM/ujsbaR0Zc9pjwxbHIKq3t0NclIiK6GMNOJ+XoIMFbs/rj83sGwVUuRUJWBaZ+uh9/n+nY21oAMKKrF86+MwUvTurV6v7x/9nDVh4iIjIZhp1OblpkAGKfHoP+Qe6oqNNg/soELN1yusMWEG0mlYjx5I3dcfRfMZc9JnxxLDYmF3To6xIRETHsEMK8XPD746OMQ9P/t+887vpfHPIrO/a2FgB4u8qRtWwafrnMra2n1xxjKw8REXUohh0CYOjH88aMfvjqvkFwc5QiKacS05bvx85TRSZ5veFdvXDu3am4oadPq/vDF8cy9BARUYdg2KEWJvcPwJanxyIqWIHKOg0e+vEo3t58Co3ajr2tBQASsQg/PjgMx19rfRV1wBB6csvrOvy1iYio82DYoUuEeDpj3WOj8ODoCADAtwcycef/4pBXYZrQ4eEsQ9ayafjs7uhW9499/2+28hAR0TVj2KFWyaRivDa9L76+fzDcHaU4nluJqZ/ux18dvMzExaZHBSJz6dTL7g9fHIuuSxh6iIiofRh26Ipu7ueP2KfHYmCIB6oatHjkp0T8e5NpbmsBhmUtspZNw94Xx7e6Xy8YQk9ybqVJXp+IiOwPww5dVYinM359dCQeHmu4rfX9wUzc8dUhk/alCfNyQebSqegf1Po6WzM/P4jwxbHQ6wWT1UBERPaBYYfaRCYV45VpffHtA0Pg4eyA5DwVpi7fj20nCk32miKRCJsXjkXCK5efm6fry1vYn4eIiK6IYYfaJaavH2KfHotBoR6obtDisZ+T8MbGk1BrdSZ7TR83w9w8+1688bLHhC+OReQb201WAxER2S6GHWq3IA8n/PLoSDw6risAYOWhLNz+ZRyyy0y7xlWolzOylk3DV/cNbnV/VYMW4YtjseFYvknrICIi28KwQ9fEQSLGkil9sGLeUHRxdkBqvgq3LD+ALammu63VbHJ/f2Qtm4ZHb+ja6v5FvxxH+OJYFFc1mLwWIiKyfgw7dF1u7O2LLc+MxdDwLqhWa/HEqiS8uuEEGjSmu63VbMnUPjjz1uTL7h/27i6EL46Fjp2YiYg6NYYdum4BCieseXgEnhjfDQDw0+FszP7yELJKTXtbCzCs3p61bBoOLp5w2WO6sRMzEVGnxrBDHUIqEeOlyb3xw4PD4Okiw8mCKtzy2QFsMtMq5kEeTshaNg2rHxp+2WO43hYRUefEsEMdalxPH2x5eiyGRXiiRq3FwjXH8PL6VLPc1gKAUd29kfHOFCyc0P2yxzD0EBF1Lgw71OH8FY5Y/dBwLJzQHSIRsDo+BxM/3Is/j+ebZRJAB4kYz9/cC0demYiefq6XPY6hh4ioc2DYIZOQNgWOHx8chgCFI/Ir6/HM2uO49YuDOJJZbpYafN0c8dez4/D74yOveBxDDxGRfWPYIZMa28MHu58fjxcn9YKLTILkPBXu/F8cHv3pKDLN0IEZAAaHeeLcu1Px9qz+VzyOoYeIyD6JBEHo9ONyq6qqoFAooFKp4O7e+lpM1+LiN86sZdM67Ly2qqRajY93pmPtkRzoBUAqFuG+EWF4ZmIPdHGRmaWGitpGfPBXGlbH51z1WP6bERFZt7a+f1t9y05+fj7uu+8+eHl5wcnJCQMGDMDRo0eN+wVBwGuvvYaAgAA4OTkhJiYGGRkZFqyYLsfHTY53bx2A7YtuwI29fKDVC1h5KAs3fPA3vt53zqRLTjTr4iLDu7cOQOzTYzBzYOAVj2VLDxGRfbDqsFNRUYHRo0fDwcEBW7duxalTp/Dhhx+iS5cuxmPef/99LF++HF999RXi4+Ph4uKCSZMmoaGBs+daqx5+blgxfxh+XjAcfQLcUd2gxbtbziDmo73YnFIAczQ29gtU4NM50YhbMgGPjet2xWMZeoiIbJtV38ZavHgxDh48iP3797e6XxAEBAYG4vnnn8cLL7wAAFCpVPDz88PKlSsxZ86cNr0Ob2NZjk4v4PekPHz4VxqKqtQAgOhQD/xrWh8MDvM0Wx21ai1+S8zD6xtPXvVY/lsSEVkHu7iNtXHjRgwZMgR33HEHfH19ER0djW+++ca4PzMzE0qlEjExMcZtCoUCw4cPR1xc3GXPq1arUVVV1eKDLEMiFuHOISH4+4XxeDamJ5xlEhzLqcTsL+Pw5Kokky8u2sxFLsXcUeE49+5UfH3/YIhFlz+2uaXHiv9OICKii1h12Dl//jy+/PJL9OjRA9u3b8fjjz+Op59+Gj/88AMAQKlUAgD8/PxaPM/Pz8+4rzVLly6FQqEwfoSEhJjum6A2cZZJ8UxMD+x5YTzmDA2BWATEphYi5qO9eHvzKajqNGapQyIW4eZ+/ji/dBo2LxwDP3f5ZY+NWGJYhsJcEyYSEdG1serbWDKZDEOGDMGhQ4eM255++mkkJCQgLi4Ohw4dwujRo1FQUICAgADjMXfeeSdEIhF++eWXVs+rVquhVquNj6uqqhASEsLbWFbkjLIK78Sexv6MUgCAwskBT0/sgftHhEEmNW9GV6oa8O6W09h4laUvdj0/Dt18Lj+JIRERdSy7uI0VEBCAvn37ttjWp08f5OQYhg37+/sDAIqKilocU1RUZNzXGrlcDnd39xYfZF16+7vjpwXD8cODw9DLzw2qeg3e2nwKN328F1tTC816C8lf4Yjld0fj1L8n4aXJvS573MQP9yJ8cSy+3HPObLUREdHVWXXYGT16NNLS0lpsS09PR1hYGAAgIiIC/v7+2LVrl3F/VVUV4uPjMXLklWfNJdswrqcPtjwzFstuGwAfNzmyy+rw+Kok3PFVHI7lVJi1FmeZFE+M747z707Ftw8Muexx7207wxFcRERWxKrDzrPPPovDhw/j3XffxdmzZ7F69Wp8/fXXePLJJwEAIpEIixYtwttvv42NGzciNTUVDzzwAAIDAzFr1izLFk8dRiIWYc6wUOx5YTyentgDjg5iHM2uwK1fHMLCNceQW15n1nrEYhFi+voha5mhX8+VMPQQEVmeVffZAYDNmzdjyZIlyMjIQEREBJ577jk8/PDDxv2CIOD111/H119/jcrKSowZMwZffPEFevbs2ebX4NBz26JUNeA/f6Xh96Q8CAIgk4gxf3Q4nrixOxRODhapqaiqAcPf3XXV406+OQkucqkZKiIisn9tff9uV9g5ffo01q5di/379yM7Oxt1dXXw8fFBdHQ0Jk2ahNmzZ0Muv/zoFWvFsGObThao8O6W0zh4tgwA0MXZAc9M7IF7R4TBQWKZRsv6Rh3u+joOKXmqKx733uwBuGtoqJmqIiKyTx0adpKSkvDSSy/hwIEDGD16NIYNG4bAwEA4OTmhvLwcJ06cwP79+1FVVYWXXnoJixYtsqnQw7BjuwRBwN9pxXh3yxmcLa4BAER4u2DxlN64ua8fRKIrTJhjQnq9gOd+PY4Nx688ggvg/w0iomvVoWEnIiICL774Iu655x54eHhc9ri4uDh8+umniIyMxMsvv3xNhVsCw47t0+r0WJuQi493pKOsthEAMDzCE69M64PIYA+L1SUIAn5JyMXiP1Kveuz5d6dCfKXZDImIqIUODTsajQYODm3vC9He4y2NYcd+VDdo8NXec/h2fybUWj0AYNbAQLw4uTeCPJwsWltmaS1u/M+eqx731X2DMLl/wFWPIyLq7EzSZ6c1giBY7FZBR2HYsT/5lfX4cHsa/jiWDwCQS8VYMCYCj4/vBjdHywbx+kYdnll7DH+dKrrqsfx/Q0R0eWYLOzKZDMnJyejTp8/1nMaiGHbsV2qeCm/HnkJ8ZjkAwMtFhoUTuuOuoaFwkkksWpteL2D7SSUeX5V01WNPvDkJrhzFRUTUQoeHneeee67V7Z9++inuu+8+eHl5AQA++uijayjXshh27JsgCNh5uhhLt5zG+VLDwqIezg64d3goHhgZDj93RwtXCJwurMKUT/df9bgbe/lgxfxhZqiIiMj6dXjYEYvFiIqKuqSD8t69ezFkyBC4uLhAJBJh9+7d11W4JTDsdA6apk7M3+w7j5ymiQgdJCJMjwzEg2Mi0D9IYeEKgeLqBny4PR2/HM296rGZS6fa/C1kIqLr0eFhZ9myZfj666/x7bffYsKECcbtDg4OSE5OvmQNK1vCsNO56PQCdpwqwncHziMh68KSEyO7emHBmAhM6O1r8VFRDRod1h/Lx5I2jOJ6fXpfzB8dYYaqiIisi0n67CQkJOC+++7D9OnTsXTpUjg4ODDsXAHDjvVLzq3EdwcyEZtaCJ3e8KPQ1dsF88dEYPagIDjLLNtPRq8XsC+jBA//eBQa3dV/VPn/jIg6E5Osej506FAkJiaipKQEQ4YMwYkTJ9iMTjYtKsQDy++Oxv6XbsSjN3SFm6MU50tr8eqGExi5dDfe33YGRVUNFqtPLBZhfC9fZLwzFdsWjcW0AVcekt68FtevCVe/DUZE1Flc82istWvXYtGiRSgpKUFqaipbdlrBlh3bU6vWYt3RXHx/MMtq+/WUVKvx0+FsLN+V0abj2beHiOyVWYae5+XlITExETExMXBxcbnW01gcww79U3O/nu8PZOJIVrlx+4iunnhoTFer6dfz5/F8/Pfvs8gtr7/q8Y+O64olU2x3iggion8y2zw79oBhh66ktX49Ed4ueHB0OGYPDrZ4vx5BELA/oxQ/HMrCrjPFbXpOxjtTLLZYKhFRR+nwsDNgwADceeedmDdvHkJCQjqsUGvAsENtUVBZjx/isrA6PgfVDVoAgMLpwnw9/grLz9dTVqPGpuQCrD+Wj+SrrLzejP83ichWmWSeHU9PT1RWViImJgYPP/wwZs6cCanU9md1Zdih9mju17PiUBayywz9eqRiEaZHBWKBlfTrAYBzJTXYcCwf3x/IRG2j7qrH73xuHLr7upqhMiKijmGSsJOXl4cjR47g+++/x9atW9GlSxc88MADWLBgAZeLaAXDjn3T6QXsPF2E7/a37NczPMITD43tiolW0K8HMAxfP5pdgfXH8rDmSNtGafH/KxHZApOEHaVSCV9fXwBAYWEhVq5ciRUrVuDcuXMYPnw4HnroITz44IMd8x2YEcMOXa+UPEO/ns0p1tmvp1mDRofdZ4rxw6Es43phVzK2hzd+WjDcDJUREbVfh4cdiUSCwsJCY9i52J49e/Ddd99h/fr1qKmpufaqLYRhhzpKc7+eNfE5qLqoX889w0Mx10r69TQrr23E5pQCvPbnyTYdf3DxBAR5OJm4KiKitjN5y87lXrQjw4K5MOxQR6tVa/FbYh6+P5jZol/PLZEBeGhsV6vp19Mss7QW65PysHz32bYdz7l7iMgKdHjYmT9/PpYvXw43N7cOK9JaMOyQqRj79RzIxJFM6+3X00wQBCRmV2DFwSzEpha26Tn8v01ElsJ5dtqBYYfMoblfT2xKIbRN/XrCvZzx4JgI3G5F/XqaqbU6/H2mGI/9nNSm47+8dxCmXGU5CyKijsSw0w4MO2ROhap6/HAoG6vjs1v067l7WCjmjgpDgML6+sVU1Dbi96Q8vB17uk3Hn3xzElzk1hXeiMj+mD3szJ07F7m5udi9e3dHnM6sGHbIEq7Ur2fBmK4YEGxd/XqaZZfV4sO/0rExuaBNx/P/PhGZitnDzssvv4zCwkKsWLGiI05nVgw7ZEk6vYBdp4vw7T/69QyL8MRDYyIwsY8fJFbUr6eZIAiIzyzHnK8Pt/k5/Dkgoo7E21jtwLBD1iI1T4XvDpzH5ov69fi7O+K2QUG4fXAwuvpY5wzHjVo9fk/Kw5I/Utt0/MyBgfh0TrSJqyIie8ew0w4MO2Rtmvv1rE3IQWWdxrh9SFgX3DEkGNMiA+FqpX1iVHUarDyUhY93prfp+JXzh2J8r8tPaUFEdDkmCTunTp3Cf//7X8TFxUGpVAIA/P39MXLkSDz11FPo27fv9VduAQw7ZK3UWh12nirGusRc7EsvQVNjD5wcJJg6IAB3DAnG8AhPq53zJre8Dl/tPYdV8TltOv7IyxPh6249Ey8SkXXr8LCzdetWzJo1C4MGDcKkSZPg5+cHACgqKsKOHTuQmJiIP//8E5MmTeqY78CMGHbIFihVDfjjWB5+O5qH86W1xu2hns64fXAwZg8OttoZjgVBwPHcSnyx5xx2nCpq03My3pkCB4nYxJURkS3r8LATFRWFmTNn4t///ner+9944w388ccfSElJubaKLYhhh2yJIAhIyqnAuqN52JRcYFzRXCQCRnfzxh1DgjGpnz8cHSQWrrR1Gp0ee9NK8MH2NKQVVbfpOZyxmYha0+Fhx8nJCcePH0evXr1a3Z+WloaBAweivr7+2iq2IIYdslV1jVpsTVViXWIuDp+/MJLLzVGKGVGBuGNICKKCFVYbFFT1GmxNLcTL61ONt+iuhj9LRNSsre/fbe7hGB4ejtjY2MuGndjYWISFhbW/UiK6Zs4yKWY33cLKKavDb0l5+D0xD/mV9VgVn4NV8Tno4euKO4YE49boYPi4yS1dcgsKJwfMGRaKOcNCkVtehz+P5+M/f125YzP/iCCi9mpzy866detwzz33YMqUKYiJiWnRZ2fXrl3Ytm0bVq9ejdmzZ5u0YFNgyw7ZE71eQNz5Mvx6NBfbTiih1uoBABKxCDf28sUdQ4Ixobev1faHEQQBqfkq/JGUj5WHstr8PP6MEXU+JhmNdejQISxfvrzV0VjPPPMMRo4cef2VWwDDDtkrVb0Gm1MKsO5oHo7nVhq3e7nIMCs6CHcMCUZv/477P9/RNDo99meU4NeEPGw7qWzz8/jzRtQ5cJ6ddmDYoc4go6gavyXm4fekfJTWqI3bI4MVuGNwMGZEBUHh7GDBCq+sqkGDbalK/JaYhyNZ5Vd/AgBXuRQn3rS9EaJE1DZmCTvLli3DY489Bg8Pj2s9hVVg2KHOpHk01LrEXOw6XWycqVkmFePmvn64Y0gIxnT3tsolKprlV9bjz+P5iE0pxMmCqjY9J1DhiENLJpq4MiIyJ7OEHXd3dxw/fhxdu3a91lNYBYYd6qzKatTYcLwA647m4ozywjDwAIUjZg8Kxu2DgxHu7WLBCq8ut7wO208qsSW1EEk5lW16DoMPkX0wS9hxc3NDcnIyw85lMOyQrRAEAScLqrDuaC42HC+Aqv7CEhXDwj1x+5BgTBsQABcrXaKiWVFVgzH4XDwU/0oUTg5Ifv1mE1dGRKbAsNMODDtEFzRodNh5ugjrjuZhf8aFJSqcZYYlKu4cEoKh4V2sdu6eZuW1jdhxSonYVCX2pZe0+Xn8WSWyHWYJO7m5uQgMDIREYp0ztbYVww5R65SqBvyelIffEvOQedESFeFehiUqbhsUjEArXaLiYqp6DXafKUJsihI7T7dtuQqAP7dE1s5kYadr165ISEiAl5dXi+2VlZUYNGgQzp8/f20VWxDDDtGVCYKAxOwK/Ho0F7EphS2WqBjT3Rt3DgnBTX39rHaJiovVqrXYk1aC2NQCbEnlcHYiW2aysCMWi6FUKuHr69tie1FREUJDQ6FWqy/zTOvFsEPUdnWNWmxJVWLd0VzEZ17oF+PuKMXMgYa5ewYEWe8SFRdr0OhwIKMUm1MKsOF4QZufx59nIuvQ4WFn48aNAIBZs2bhhx9+gEKhMO7T6XTYtWsXduzYgbS0tOss3fwYdoiuTXZZLX5PNNzmKlA1GLf38nPDHUOCMSs6CN6u1rVExeVodHrEnSvDpuQCrEvMa/Pz+LNNZDkdHnbEYsPU8iKRCP98ioODA8LDw/Hhhx/illtuuY6yLYNhh+j66PQCDp0rxbqjhpmOG5uWqJCKRRjfyxczBwYipo8fnGTWf5sLMHw/CVnl2JhcgNXxOW1+Hn/OiczLZLexIiIikJCQAG9v7+su0low7BB1HFW9xtg6knzREhXOMglu6uuHGVGBGNvDBzKpda7N9U96vYDkvEr8ebygXWt1nX93KsRWPDEjkT3gchHtwLBDZBrpRdX483g+NiYXILe83rjdw9kBU/r7Y3pUIIZHeFn1bM0XEwQBpwqrsOFYPr7Zn9nm5514cxJcrXyOIiJb1KFhZ+3atZgzZ06bXjg3Nxc5OTkYPXp026u1MIYdItMSBAHHcyuxMbkAm1MKUVJ9YSCDn7sc0wYEYubAQEQG20bH5mZni6ux4VgB/vv32TY/Z8ezN6CHn5sJqyLqPDo07IwbNw7FxcWYP38+pk+fjj59+rTYr1KpcPDgQfz888/YsWMHvvvuO8yYMeP6vwszYdghMh+dXkD8+TJsTC7AltRCVDVojfvCvJwxIyoQM6ICbS4Q5JTVITa1EO9tO9Pm57x/eyTuHBJiwqqI7JtJRmN99tln2L17N1xcXODn5wdHR0dUVFRAqVTC29sb8+bNw7PPPgs/P78O+0bMgWGHyDLUWh32pZdiY3IBdp4qQr1GZ9zX298NMwYGYnpkIEI8nS1YZfsVquqx7YQS/9meZpyT6GqGRXji10dHmrgyIvtisj47paWlOHDgALKzs1FfXw9vb29ER0cjOjraOGLL1jDsEFleXaMWO04VYVNyAfaml0Cju/CraXBYF8yICsTUAQHwcbONoezNSmvU2HGqCF/uOYec8ro2P4+/M4iuzmRhZ+7cuViwYAFuuOGG6y7SWjDsEFmXyrpGbDuhxMbkAsSdL0PzbymxCBjd3RvTowIxqZ8/FE4Oli20nVR1Guw8XYQfD2e3GKl2Nfz9QdQ6k4WdWbNmYcuWLQgLC8P8+fMxb948BAYGXnfBlsSwQ2S9iqoasDmlEBuTC1oEBJlEjPG9fDBjYCAm9radOXya1ai1+PtMMdYl5rVrodLMpVNtqhM3kSmZdOh5SUkJfvrpJ/zwww84deoUYmJisGDBAsycORMODrb1lxbAsENkK7LLarEpuQAbkwuQXlRj3O7SNIfPzIFBGNPDGw4S27ql3qDRYV96Cf5MLkBsSmGbn3fmrck2sR4ZkamYbZ6dpKQkrFixAt9++y1cXV1x33334YknnkCPHj2u57RmxbBDZHvOKKuw8bgh+ORVXJjDp4uzA6YMCMCMqEAMC/e0uYn9GrV6HDpXii2phfj1aNuXrdi8cAz6BymufiCRHTFL2CksLMSPP/6IFStWIC8vD7Nnz0Z+fj727t2L999/H88+++y1ntqsGHaIbJcgCEjKqcSmpjl8SmsuzOHj7+6IWyIDMGNgoM0sTnoxrU6PI1nl2HZCiR/jstv8vPtGhOLtWQNMWBmRdTBZ2NFoNNi4cSNWrFiBv/76C5GRkXjooYdwzz33GF9o/fr1ePDBB1FRUXF934WZMOwQ2QetTo/D58uxMTkfW08oUX3RHD4R3i6Y3jSHT3dfVwtWeW30egHHciux7URhu2ZvBvj7h+yXycKOt7c39Ho97r77bjz88MMYOHDgJcdUVlYiOjoamZnt+4G0FIYdIvuj1uqwN63EMIfP6SI0aPTGfX0D3A1z+EQFIsjDyYJVXhtBEHBGWY3tJ5X4+XBOi9asq+HvIrInJgs7P/30E+644w44Ojped5HttWzZMixZsgTPPPMMPvnkEwBAQ0MDnn/+eaxduxZqtRqTJk3CF1980a6JDRl2iOxbrdowh8/G5ALsSy+BVn/h196QsC6YMdAwh4+3q23N4dMst7wO208qsf5YPk4WVLX5efy9RLbO7hYCTUhIwJ133gl3d3fceOONxrDz+OOPIzY2FitXroRCocBTTz0FsViMgwcPtvncDDtEnUdFbSO2nlBiY3I+4jPLjXP4SMQijOrmhRlRgZjU3x/ujrY3shQwTGK463QRNqcUYn9GaZufd/LNSXDhYqVkY+wq7NTU1GDQoEH44osv8Pbbb2PgwIH45JNPoFKp4OPjg9WrV+P2228HAJw5cwZ9+vRBXFwcRowY0abzM+wQdU5KVQM2pxhGdKXkqYzbZVIxJvTyxYyBgZjQ29dmh3fXqLXYk1aMbSeU2NyOIe3fPDAEN/W1rWV/qHOyq7Azd+5ceHp64uOPP8b48eONYWf37t2YOHEiKioq4OHhYTw+LCwMixYtuuxoMLVaDbX6wj3uqqoqhISEMOwQdWKZpRfm8DlbfGEOH1e5FDf39cP0gYEY09325vBpptbqEHeuDNtPFmHNkZw2P6+Hryt2PDfOhJURXbu2hh2rb7Ncu3YtkpKSkJCQcMk+pVIJmUzWIugAgJ+fH5RK5WXPuXTpUrz55psdXSoR2bAIbxc8PbEHFk7ojtOF1diYXIBNyQXIr6zHH8fy8cexfHg4O2BK/wBMjwrA8AgvSGxoDh+5VILxvXwxvpcv3pnVH8dyK7D9ZBG+3X8e+iv8yZtRXMM/3MjmWXXYyc3NxTPPPIMdO3Z0aIfoJUuW4LnnnjM+bm7ZISISiUToG+iOvoHueGlSLxzLrcDG4wWITS1EaU0j1hzJwZojOfBxk2PagABMjwrEoFAPm5rDRywWYXCYJwaHeWLJlN5IK6rGXyeL8EtCLvIr66/4XAYfskVWfRtrw4YNuPXWWyGRXLhfrtPpIBKJIBaLsX37dsTExLT7NtY/sc8OEV2NVqdHfGY5NiUXYOsJJVT1GuO+IA8nTI8KxPSoAPQNcLep4PNPueV1+OtUETYez0fyRf2Yrubcu1NtqqWL7INd9Nmprq5GdnbLWUPnz5+P3r174//+7/8QEhICHx8frFmzBrNnzwYApKWloXfv3uygTEQm06jV48DZEmxKLsRfJ5WobdQZ93X1ccH0SMMcPrY4eeHFymrU2HW6GLGphdjbjsVKDy2egEAbnL+IbI9dhJ3WXNxBGTAMPd+yZQtWrlwJd3d3LFy4EABw6NChNp+TYYeIrlWDRoe/zxRjU0oBdp0uhlp7YfLCPgHumB4VgOmRgQjxdLZgldevVq3F3vQSbDuhxMbkgjY/7+1Z/XHfiDATVkadWacJO82TCq5Zs6bFpIL+/v5tPifDDhF1hBq1FjsvM3nhwBAPTI8KxC2RAfBzN/+krB2pUavH4fNl2H5SiVXxbR/Z5ekiQ9KrN5mwMups7DbsmALDDhF1tMq6Rmw7ocSmlALEnSszjngSiYBh4Z6YMTAQU/oHwNNFZtlCr1Pzml1/nVTif/vOt+u5/L1I14thpx0YdojIlIqrG7A1VYlNyQU4mn1hgWSJWIQx3b0xPSoQN/fzs9lZm5sJgoCM4hpsP6HEj4ezUVLNNbvItBh22oFhh4jMJb+yHrEpBdiUXIjU/ItmbZaIMb6XD6ZHBWJiH184y6x6ZpA2ya+sx18nlVh7JBdpRdVtft75d6dCzJFd1AYMO+3AsENElpBZWovNTbM2Z1w0a7OTgwQxff0wPTIA43r5QC61zeUqLlZe24hdp4vwe1IeDp8vb/PzUt+4GW423uJFpsOw0w4MO0RkSYIgIK2oGpuSDS0+OeV1xn1ujlJM7ueP6VGBGNXNC1IbXa7iYnWNWuxNK8Gfxwuw7eTlZ7v/p70vjkeYl4sJKyNbw7DTDgw7RGQtBEFASp4Km5ILsDmlEMqqBuM+TxcZpg7wx/TIQAwN97SLWz0anWFk1+bkQvxyNLfNz1sxfyhu7OVrwsrIFjDstAPDDhFZI71ewNHsCmxKLsCW1EKU1TYa9/m7O2JapGG5iqhghU3P2txMrxeQnFeJrSeU+LodI7tevaUvFoyJMGFlZK0YdtrBnsOOWqvDyYIq5FfUo6CyHoWqBuRXGr4ur22Ei1wKd0cpFE4OUDg5wL3ps8LJARHeLugT4I4AhaNd/CIlsmVanR5x58uMy1VUN2iN+0I8nYyzNvf2d7OLn1dBEHC6sBqbUgrw5Z5zbX7e9KhAfHZ3tAkrI2vCsNMO9hh2Moqq8UtCLv44lo/yi/4avBYKJwf09ndDnwB39AkwfO7p5wZHB9vvNElki9RaHfall2JTcgF2nCpCvebCchXdfV0xo2nywq4+tr1cRTNBEHAivwqbUwraNZdPZLACG58aY8LKyNIYdtrBXsJOg0aHjccLsDYhB0k5lcbtni4ydPNxQaCHk+FD4YhADyd4ucpR16hFVb0GVfVaqOo1qGrQQFWvQVltI84W1eBsSQ10+kv/i4hFQC9/d4zq5oVR3bwwLMKTIyaILKCuUYvdZ4qxKbkAf6eVoPGi5Sr6B7nj1uhgzBwYCG9XuQWr7DiCICA5T4XNyQX49kBmm5/n5SJDImdvtjsMO+1gD2Enp6wOj/x0FGeUhrksJGIRJvT2xZyhIRjX0+eaR3CotTqcLa7B6cJqnCmswmllFU4XVl/SWiQRizAgSNEUfrwxOKwLnGRs+SEyp6oGDXacLMKmlALszyg1/qEiFYswvpcPbhsUjIl9fO1iKDvQPHtzBTYlF2Lloaw2P89VLsWJNyeZrjAyG4addrD1sLM3vQRPrzkGVb0G3q4yLBjTFbMHB8HXzTTr7wiCgOJqNY5kluPQuTLEnStFVlldi2NkEjGiQz0wurs3JvbxRd8Ad7voR0BkK8prGxGbUoDfkvKRnFtp3K5wcsD0qADcNigY0SEedvNzqdMLOJpVjs0phfjpcHabn+csk+DUvyebsDIyJYaddrDVsCMIAr7aex4fbD8DvWBYaPCr+wbDX2H+RQbzK+sRd64Mh86V4tDZshbDZQEgyMMJN/X1w019/TAswhMOdjBXCJGtOFtcjd+T8rE+Kb/Fz2ZXHxfMHhSMW6ODEOjhZMEKO5ZWp0d8piH4rDnS9oVKw72csefFG01YGXU0hp12sNWw8/qfJ/BDnOEvmDlDQ/DmzH5W0TwtCAKyyupw8Gwp9qaXYH9GCRo0F/oRuDtKcWNvX8T08cP4Xj7s60NkJjq9gLhzZfg9KQ/bTiiNHZtFImBkVy/MHhSMyf394SK3/aUqmml0esSdK8PmlAL8lpiHVrogtmpib198N2+oaYuj68aw0w62GHa2nVDisZ8TIRIB/57ZH/cND7Xa5uj6Rh0OnC3FjlNK7Dpd3GKuEAeJCCO6euHmvn6Y1N/fZLfeiKilGrUWW1MLL1m+wVkmweT+/rh9UDBGdPWyi4kLmzVq9Th4thSbUgqw8XgBtG1MPvNGheONGf1MXB1dC4addrC1sKNUNWDyp/tQWafBo+O6YsmUPh12blPT6QUcz63AX6eKsONUEc6X1Br3iUXAiK5euCUyEFP6+6OLi8yClRJ1HrnlddhwLB+/J+W16H8XqHDErYOCcNugYHSzk2HszRo0OuzPKMXmFMOEjRpd294K3789EncOCTFxddRWDDvtYEthR68XcP/38Th4tgz9g9zxx+OjIZPabv+XcyU12HmqCFtPKHH8ok6UUrEIY3p4Y3pkIG7q5wd33uoiMjlBEJCUU4HfEvOxOaWgxcSFA0M8MHtwMKZHBsDD2b7+EGnQ6LAnrRibUgoRm1LY5uetfmg4RnX3NmFldDUMO+1gS2Hnm33n8c6W03BykGDz02Ps6q+t3PI6bE4pxKbkApwqrDJul0nFGN/TB9OjAjGxjy+cZfbTn4DIWjVodNh5ugi/J+Zh30XD2GUSMWL6+uK26GCM6+Vjd4MN6hq12HW6GLEphe1apPTIyxPh687b8ObGsNMOthJ2KusaMWLpLjRo9Fh62wDcPSz0us9prc6V1GBzciE2Jufj3EW3upwcJIjp64dbowNxQ49rnz+IiNquuLoBG48bOvg2z+UFAN6uMsyICsJtg4LQL9D+ppeoUWux63QRNiUXYufpojY/79S/J/GPMjNh2GkHWwk7X+45h/e2nUHfAHfEPj3G7n6xtEYQBJxRVmNTcgE2pRQgt7zeuM/bVY5ZAwMxe3Aw+gR03L8bEV3eyQIV/kjKx5/H81Fac2GwQW9/N8weFIyZ0YF2OdBAVa/BzlNF2JhcgL3pJW1+XubSqZ3id7WlMOy0gy2EHY1Ojxve/xuFqgb8544o3D44+HrLszmCICAlT4X1x/KxMbmgxSzOfQPcMXuwfU2LT2TNNDo99qWX4I+kfOw4VYRGnWF6CbEIuKGnD2YPCsZNff3scg29yrpG/HWyCOsSc5GQVdGm54zt4Y2fFgw3cWWdD8NOO9hC2NmcUoCnVh+Dt6sMBxdPsIr5dCypUavHnrRi/J6Uh91nio0jKZqnxZ89KBgT7GhafCJrpqrTYFNKAX5PysOxi9blc3OU4pbIAMweFIzBYV3ssoWjrEaN7SeL8N2B8y1uuV/J6oeHY1Q3dmzuCAw77WALYee2Lw4iKacSz0zsgWdv6nm9pdmVitpGbEw2/KJNyVMZt3s4O2B6ZCDuHBKCAcEKC1ZI1HmcK6nB+qR8/JGUhwLVhdmaw7yccVt0MG4bFIQQT2cLVmg6xdUN2HZCiQ+2paFarb36EwBkvDPF7jp5mxPDTjtYe9hJzq3EzM8PwkEiwsHFE+zyfnhHyShqmhb/WB6KqtTG7f2D3HH3sFDMiArkjM1EZqDXCzh8vgy/J+Vj64lC1DXqjPuGR3jijiEhuCUywC5vcwGG+dB+PZqLj3akt/k57N/Tfgw77WDtYefdLafx9b7zmBEViOV3R3dEaXZPpxdw8Gwp1iXmYfsJpbE/gbNMgumRgbh7eCiighX8xUJkBrVqLbadUOL3pDzEnS9D87uOt6sM940Iw30jwuy2r51OL2BPWjG+3HMOR7Pb1r/njydGYVBoFxNXZh8YdtrB2sPO5E/24YyyGsvvjsaMqMCOKK1TKa9txB9JeVhzJKfFPfU+Ae64Z1gIZkYHcdJCIjPJr6zH+qQ8rIrPQWHTbS6ZVIxbBwZhwdgI9PRzs3CFppNbXodV8Tn4au+5Nj/n/LtT7WrJjo7GsNMO1hx2iqoaMPzdXRCJgMR/3QRPLqFwzQRBQEJWBdYcyUFsaiEatYbWHkcHMW6JDMTdw0IxKNSDrT1EZqDR6bEltRDfHchs0ddubA9vPDS2K27o4W23P4tqrQ7bTijxU1x2m1t7Pr4rCrdGd75RuFfDsNMO1hx21h3NxYu/pSAyWIGNT43pqNI6vcq6Rqw/lo81R3KQXlRj3N7b3w1zR4Vj1sAgOMnssy8BkTURBAFHsyvw3f5M/HVKaVyVvIevKxaMicCs6CC77dcDAKcLq7AqPhu/JOS2eX0u9u25gGGnHaw57Cxccwybkgvw1I3d8cKkXh1VGjVpXgtozZFcbE4pQIPG0NqjcHLAnKEhuG9EmN2OHCGyNjlldVhxKBO/JuSitqlDs6eLoV/P/SPC4ONmn/16AMNszeuP5WPV4ewWs1RfyXdzh2BiHz8TV2bdGHbawVrDjl4vYPDbO1BRp8Gvj47EsAjPDquNLqWq02BdYi5+jMtGTrlh5WexCJjYxw/zR4VjZDcv/jVFZAZVDRr8ciQXKw9lIb/SMGu6TCLGzIGBWDA2Ar397XfGdEEQkJhdgZ8OZ2Nr6oXBFVfTWVt7GHbawVrDTmqeCtP/ewCucimOvXYT52IwE51ewN9nivFDXBb2Z5Qat/f0c8XcUeG4NTqI694QmYFWp8e2k0p8dyCzxWSFY7p7Y8GYCIzr6WPXnXdLa9T49WguVsfnIK+i/upPAJDwSoxdt4D9E8NOO1hr2Fkdn4OX16dymnELOltcjR8OZeP3pDzjPCHujlLcNTQED4wM5y0uIjNJzK7A9wcysfVEobFfTzcfFzw4JgK3RQfbdR87nV7AvvQS/HQ4G3+nFaMt79pvzuiHuaPCTV6bpTHstIO1hp3X/zyBH+Ky8cgNXfHy1D4dVhe1X1WDBuuO5uHHuCxklxlucUnEIkwbEIDHxnVD30D7bVYnsia55XX44VAWfknINc5S3MXZAfcOD8MDI8Pg627fk67mltdhzZEc/JKQi7KL1ge8HDe5FKlvTjJDZZbBsNMO1hp27vpfHOIzy/HhHVGY3QkX/rRGer2APenFWHGw5S2ucT198Ni4bhjR1bNT3jcnMrfqBg1+PZqHFQczjbd4HCQiTI8KxIIxEegXaN9LxDQPX191OAdHssrb9Bx7XJqCYacdrDHsCIKA6Ld2oLJOg80Lx6B/kH3/4NqiE/kq/G/fecSmFBib1aNCPPD4uG64ua+fXfclILIWOr2Av5r69Vw8Z83Irl5YMCYCE3r72v3PYpqyGj8fzsaaIznQ6q/+lp7yxs12M5Eqw047WGPYaZ5MUCIW4eSbk+x6nglbl11Wi2/2n8e6o3lQN01U2NXHBY/e0BWzooO48jqRmRzPrcR3BzKxJbUQuqY3/QhvFzw4OhyzBwfb/cCCGrUWG47lY8XBzDatwH7s1ZvQxcYnqmXYaQdrDDt700sw9/sj6Objgl3Pj++wmsh0SqrVWHkoEz/FZaOqwdCXwM9djofGdMX9I8MYWInMJL+yHj8eysLqIzmobvpZVDg54L4RoXh8fHe4yu079DTPH7biYBY2pxRe9fi/XxiPCG8XM1TW8Rh22sEaw87X+87h3S1nMG1AAD6/d1CH1USmV6PWYk18Dr49cN648rqvmxwLJ3THXUNDIZPa1z1zImtVq9Zi3dFcrDh0YWBBgMIR/57ZHzf17RyT8ZXVqLE2IRcfbE+76rFHXp5ocx28GXbawRrDzku/JePXo3l4NqYnnonp0WE1kfmotTqsT8rHZ7vPGidGC+7ihGcm9sCt0UGQ2llHQSJrpdML2HFKiXe3nDFOGDqlvz/emNEPfjb25n6tqhs0+M/2NPwQl33VY8+8NdlmWqLb+v7N37ZWqnk14KAuThauhK6VXCrBnGGh2P3COLw5ox983OTIq6jHi7+lYNIn+xCbUgh9GzoTEtH1kYhFmNw/ANsX3YDHxnWDRCzC1hNKxHy4Fz8dzu4UP4dujg54c2Z/bF44BpHBVx7w0vvVbQhfHAttG2dvtgUMO1ZK2RR2/DvJXx32TC6VYO6ocOx78UYsntIbHs4OOFdSiydXJ+GWzw5g95kisIGVyPScZBIsntIbm54ag6gQD1SrtXh1wwnc8b84pLVxPSpb1z9IgfVPjMZbs/rDzfHKfZe6v7IVN7z/t5kqMy2GHSulrGoKOwqGHXvhJJPgsXHdsO+lG/HMxB5wlUtxqrAKD648ijv/F4eTBSpLl0jUKfQNdMcfj4/CG9P7wkUmQWJ2BaYt348Ptp9Bg0Zn6fJMTiIW4f4RYdj1/DjMGhh4xWNzyusQvjgWB8+WXvE4a8ewY4Vq1VrjCAKGHfvj7uiAZ2/qiX0v3YhHb+gKRwcxErIqMP2zA3j9zxNQ1WssXSKR3ZOIRZg3OgI7nhuHm/r6QasX8Pnf5zD5k304ZONv7G3l6+aIT+ZEY9VDw9H1KqOx7v02HuGLY202DDLsWKHmVh03udTuh0h2Zp4uMiyZ2gd/vzAet0QGQC8AP8RlY+KHe/BbYl6n6EdAZGmBHk745oEh+Oq+wfBzlyOrrA73fBuP539NRnkblmOwB6O7e2ProrF4/qaeVx0t2vvVbXhyVZKZKus4DDtWqLm/jh9bdTqFAIUT/nvPIKx6aDi6+bigtKYRL6xLxp3/i8OpgipLl0fUKUzu748dz43DAyPDIBIBvyflIeajvfgjKa9T9KmTSyVYOLEHdjx7A8b19LnisbGphTbXgZlhxwo1h50Ahp1OZXR3b2x95gYsmdIbzjIJjmZX4JbP9uONjSdR1cBbW0Sm5u7ogH/P7I/fHx+FXn5uKK9txHO/JuP+744gu+zqMxLbgzAvF6ycPxSf3zMIfu7yKx7b/ZWtWLb1jJkquz4MO1aoqNoQdnzdGHY6G5lUjEfHdcOu58dhWtOtrZWHsjDlk/1IvGjdHyIynUGhXbD56TF4cVIvyKViHDhbips/3ocv9pyFxoZaM66VSCTCtMgA7HxuHOaPDseVlhb7au85hC+OtfrWL4YdK1RVb+ic7OFsHwu1UfsFKJzw+T2D8POC4QjxdEJ+ZT3u/F8cPv/7LPvyEJmBg0SMJ2/sju2LbsDo7l5Qa/V4f1sapn92AMdyOscfHm6ODnh9ej9sbBqqfyURS7ZYdedlhh0rVKM23LJg52Qa08MbsU+PxYyoQOj0Aj7Ynob7v49HcVMndiIyrXBvF/y8YDg+ujMKXZwdcEZZjdu+PIQ/j+dbujSz6R+kwB+Pj8Lbs/rD/Qpz8/R+dRsKmmaLtzYMO1aopmnY+dUmfKLOwd3RAZ/OGYj3b4+Ek4MEB8+WYcqn+/F3WrGlSyPqFEQiEW4bFIxdz4/H9KhACALw8h+pnaYfD2AYqn/fiDDsen48bo0Ouuxxo5btxt9nrO93E8OOFaruRGFHEAQ0aHRo1Oqt/p6vJYlEItw5JASbFo5BnwB3lNU2Yv6KBHy0I53XjchMPF1k+OSugRgW4YnaRh2eXnu8U/ThuZiPmxwf3zUQn99z+QWq569MwKFz1jVXkf2/m9qgarUh7LjK7afPTn5lPRIyy3E8txKZpbXILqtFWU0jahu1uLgLilwqhrerHN6uMgR6OCHC2wUR3i7oH6RAD1/XTr94ZndfV6x/YhSWbT2DlYeysHxXBurUWrwyrQ9Eoiv0IiSiDiERi/DJXQMx5dP9SM6txEc70vF/k3tbuiyzmxYZgA3H/bDjVFGr++/5Jh6HFk9AoId1rO/IsGOFmm9judp4y05JtRp/JOVh/bF8nGnjujNqrR75lfXIr6xHcl7L5ROcHCQYEKTA6O7eGNPDG1HBik4ZfhwdJHhjRj909XHBa3+exLcHMqHW6vHmjH4QX2nYBBF1iEAPJ7w3ewAe+zkJX+09h7HdvTGqu7elyzK7127pi73pJWjUtt66NWrZbmQunWoVf4jZ9rupnaq28Q7KlXWN+HLPOfwQl4UGjeGHQCIWoX+gO4aEe6KnnytCPJ3h5+4IN7kUTjIJ9AKg1elRq9ahrFaN0ppG5JbXIbO0FhnF1TiRX4UatRZHsspxJKscH+9Mh6eLDJP7++OWAQEY0dWr073RPzAyHDKJGEvWp+Knw9nQ6PR459YBkHSy60BkCZP7B+DuYaFYcyQHi345jm2LboCni8zSZZlViKczHhvXDct3ZcBZJkFd46WjsSKWbEHWsmkWqK4l23w3tXPNLTtX6vVurQ6dLcVzvyYbl7yIClbgrqGhmDrAHx7OV/9F4OUKhHo5X7JdrxdwvrQGRzIrcOBsCQ6eLUN5bSNWx+dgdXwOQj2dcc/wUMwZGtKm17EXc4aFQu4gxvO/JmNtQi4adXp8eEeUVfwlRWTvXrulLxKyynG2uAYv/ZaMbx4Y0ul+9h4f1w2/J+Yhv7Ie80eHY8XBrEuO+eukEjf38zd/cRfpfPcAbEBza4hcKrFwJe3za0Iu7v0uHsqqBnT1dsGKeUOx4cnRuGd46HUHELFYhO6+brhneCi+uHcwEv8Vg58WDMOcoSFwc5Qip7wOy7aewZj3/sb7286gopOsaQMAt0YH47O7B0EqFuGPpHysO5pn6ZKIOgUnmQTL50RDJhFj5+li/HQ429IlmZ2TTIJXb+kDAFh1OAcr5g295JhHfko0d1mXYNixQrqm0TUSie38hfDn8Xz83x8pEARg9qBgbH56DG7s7Wuyv3KkEjHG9vDBstmRiH95It6bPQC9/d1Qo9biiz3ncOOHe/Dz4WzoOskEfNMiA/DS5F4AgLdiT6FQZZ1zXRDZm76B7lgy1dBB+e3Y0zij7Hzr2U3q548x3b3RqNNjVXw2XpzU65Jj3t1y2gKVXWDVYWfp0qUYOnQo3Nzc4Ovri1mzZiEtLa3FMQ0NDXjyySfh5eUFV1dXzJ49G0VFrfcOtxXNM+RKbKQ5NLO0Fot/T4UgAHNHhuE/d0TCWWa+W3DOMinuGhqKLU+Pxdf3D0ZvfzdU1mnwrw0ncPc3h612kquOtmBMVwwM8UB1gxYv/5HKIelEZjJvVDgm9PZFo1aPp9ccs+qZhE1BJBLhjRl9IRWLsPN0MSK8XS455ut95y1Q2QVWHXb27t2LJ598EocPH8aOHTug0Whw8803o7b2wkROzz77LDZt2oR169Zh7969KCgowG233WbBqq9fc8uO2Kr/dS54ZX0q6jU6jOzqhden97PYPWuxWISb+/lj88IxeGN6X7jIJDiSWY4pn+5H3Lkyi9RkThKxCB/cHgmZRIy/00qwoRPN8EpkSSKR4WfPx02O9KIaLN+VYemSzK67rxvmjw4HAPxrwwnLFtMKq3473bZtG+bNm4d+/fohKioKK1euRE5ODhITDff/VCoVvvvuO3z00UeYMGECBg8ejBUrVuDQoUM4fPiwhau/Nnq9gOY/yG2hZScxuxyHzpXBQSLC+7dHWsWIKKlEjHmjI7DlmbGIDFZAVa/B/d/FY2tqoaVLM7kefm5YOKE7AOCHQ52v/wCRpXi5ynH/iDAAQHpR26basDdPT+wBHzc5yi/TZ9KSEzBaddj5J5XKMO+Kp6cnACAxMREajQYxMTHGY3r37o3Q0FDExcVd9jxqtRpVVVUtPqyF7qJbD1IbaNpZcyQXADBrYBBCPC8dRWVJYV4u+PXRkZgWGQCtXsDTa491ihae2wYHAwBS81WobtBYuBqizuNotmGB0OERXhauxDLcHB2wKKbHZfdnFNWYsZqWrP/dtIler8eiRYswevRo9O/fHwCgVCohk8ng4eHR4lg/Pz8olcrLnmvp0qVQKBTGj5CQEFOW3i4Xd6i19qwjCAL2ppcAAGZdYa0US3J0MIyWmBYZAI1OwLO/HEdN0wzV9irIwwlhXs7Q6QUkZJVbuhyiTqG+UYfD5w1/TI3v5WPhaixnX9N7QmssOXeclb+dXvDkk0/ixIkTWLt27XWfa8mSJVCpVMaP3NzcDqjwytraWVR/0XHWPjlcgaoBJdVqOEhEGBLexdLlXFZzX5ZQT2coqxrwa4Lp/70tbWRXw1+Wh88z7BCZw+HzZWjU6hHk4YTuvq6WLscidp8pwvaTlx8gFOJpuaUjbGLWuqeeegqbN2/Gvn37EBwcbNzu7++PxsZGVFZWtmjdKSoqgr//5ScwksvlkMvlpiz5Ejq9AGkbhpJfnIlEsO6wo2wa3uzn7tghcwKtO5qL97alQau/9L6uo1SCwy9PvOZzO8ukmDsqHG9tPoUDZ0vx4JiI6ynV6rk0/QXV2RYpJLKU5lbucb18Ot3EgoChZeu1P08CAIZHeCI+89I/tCx5Xay6ZUcQBDz11FNYv349du/ejYiIlm9QgwcPhoODA3bt2mXclpaWhpycHIwcOdLc5V5RoaqhTcc5XLTWU6OVv1FV1RtuBymcOmbB0j+S8lFao0ZlnebSj/rrnySwi7Ohzlo7v40FAKcLDf3Q+vi7W7gSos5hT1oxAGBcz855C+u/f2cgr6IegQpH+CscL9nv7WrZme2tumXnySefxOrVq/Hnn3/Czc3N2A9HoVDAyckJCoUCCxYswHPPPQdPT0+4u7tj4cKFGDlyJEaMGGHh6luKO1/Wpg68Dhe1/lxucTVr0dx60Np6KNeios4QaJbeNgBDwz1b7LvePwh0egFrm25fDQhSXN/JrJwgCMaw0zvAzcLVENm/rNJaZJXVwUEiwuhOuCDo2eIa4zw6L0/rg6dWH7vkmEOLr71lviNYddj58ssvAQDjx49vsX3FihWYN28eAODjjz+GWCzG7NmzoVarMWnSJHzxxRdmrvTqYlMKceeQq3eEFolEkEvFUGv1UGute2Iqr6akrlQ1QKvTX/cK5M2L6J0trsGcoSEd1uRZ36jD//2egiOZ5XBykGDuqPAOOa+1ik0tREWdBjKpGD39GHaITK25VWdImKfNLuB8rQRBwKsbTkCjEzCup0+rQWf2oGDIpJa9kWTV/ypt6dTr6OiIzz//HJ9//rkZKrp2e6/QQ/2fZE1hx9pbdsK9XOAql6JGrUV6UQ36Bl7fLZO7h4Xi0LkyfHcgE0ezynH3sFCM7emDII9r69Sm1wv465QSy7aeQVZZHSRiET66M8rqhsh3pPLaRrzedN/88XHd4OhgW+urEdma0ho1fm1aj64zjsL683gB4ppGoV3ufe7DO6PMWVKrrDrsdFZyqRjVANRWHnYkYhGiQz2wP6MUu88UXXfYmR4ViKKqBry/LQ3JeSok56UCAAIUjujh54ZuPi7o6uOKQIUjfN0c4esuh5eLrEWLkiAISC+qwY5TSvyelI/MUsNs275ucnxy10CMsuMmZkEQ8PrGkyirbUQvPzc8eWN3S5dEZNf2pBXjhXUpKK1Rw8lBgqkDAixdklmp6jV4O/bUFY/JeGeKmaq5MoYdE7qxlw/+Tmt7i06z5pFN1t6yAxgmE9yfUYpfj+bhifHdr3sG5YfGdsXMgUFYl5iL7SeUOFFQhUJVAwpVDa3O3yAWAZ4ucni7yiCXipFVVgdV/YWJ9NwcpZg7MhyPje9m183LjVo9lvyRik3JBRCLgPdvj7R4szGRvVJrdXh/Wxq+O5AJAOjl54bld0fbdavxPzVq9Xhr8ymU1lx+8EjqGze3GHRjSfb7298K3Doo+JrCTvOblLWPxgKAKQP88camk8gpr8OG4/m4bVDw1Z90FT5ucjwxvjueGN8dNWotThVU4XxJDc6V1OB8SS2KqhtQXKVGaY0aesHQjFxaozY+38lBgmERnpgWGYCpAwLsOuQAhr+uHvspEXHnyyARi/DOrP6ICvGwdFlEdulscTUWrjluHAQwb1Q4Fk/p3WluGev0AjYcy8c7W05fdlkIADjx5iSr+t1rPZXYoWsd9SNvCjv1HTTKyZScZVI8eWN3LNt6Bu9vS8PN/fw79D+4q1yKYRGeGBbheck+nV5AWa0axVVqlNU2okGjQ6inM7r6uHTIvD+2IDm3Es+vS8bZ4hq4yCT4/N5BGN/L19JlEdkdQRCw5kgu/r35JBo0eni6yPDB7ZGY2MfP0qWZhV4vYNtJJT7akY6zxVde9iFz6VSrm2uIYceEvK5xXgH3pnlrLr4dY83mjQrHqvhs5JbX4/9+T8F/7442y390iVhk6LvjdumcDvautEaND7al4ZejhuH0/u6O+H7e0OvuN0VEl6qsa8Ti31Ox7aRh+pOxPbzx4R1R8HW3/989giBgT3oJPvwrDSfyr7yO5G2DgvDRnQPNU1g7MeyYkPwa+0w0T35XWXf9E+mZg6ODBJ/cFY27/heH2JRCDAhS4LFx3Sxdll1q1OqxKj4bH+1IR3WDYXLE26KDsHhq704Z+ohMLe5cGZ795TiUVQ1wkIjw0qTeWDAm4rr7J9qCw+fL8J/tacYFTq8k8V8x8HI178oE7cGwY0KSa2zd6OJsaBGqqLONlh0AGBzWBa9M64M3N53Csq1nIBWL8NDYrpYuy26U1zZizZEc/BiXhaIqQ/+kfoHu+PfMfhgcduktPiK6Po1aPT7dlY4v9pyDIABdvV2w/O5o9LfzSUkBw+3x//yVhv0ZpVc9dsmU3njUBv64ZdgxoWtdyNPDGHZso2Wn2bxR4aiobcTy3WfxduxplFSr8eKkXtc92WBnll5UjRUHM/FHUr5xKgIfNzkWxfTAnKGhVr9YLJGtySqtxdqEXPyWmGcc+HDXkBC8Nr2vcdZ4e5WmrMaHf6Xhr1OXX8yzmZtcitQ3J5mhqo5h3/9yFnat/VYu3MaynZYdwPD9PndzL0jEYny8Mx3/23cex3IrsXxOdKtrpVDrClX1iE0pxOaUQhzPrTRu7x/kjgVjIjBtQCCHlRN1oAaNDttPKrHmSA4On7+wgKW3qxxvzOiLWyIDLVid6WWV1uLjnen483hBm463xg7IV8OwY4W62GjLTrNnYnqgh58rXvrNsERDzEd7sSimB+aOCreaOResTXF1A7amKrE5pQAJWRfuj4tFwKR+/nhwTASGhHWxuV8wRNbsjLIKa4/kYv2xfOOAEJHIsJjnnKEhmNjHz65/ZxVU1uOtzaew9YTyqscGeTjhwP/daLO/gxh2rJBHU8uOLfXZ+aepAwLQ298Nz/6ajOTcSrwdexq/JORi4cQemNrfv9Pf2mrQ6JCQVY4DGaXYl1FqnLOj2dDwLpgeFYjJ/f3Z8ZioA9WqtdiUXIC1CbktWk4DFY64c2gI7hgScs1L1NiCs8U12H5SiQ+2p7Xp+Ldn9cd9I8JMXJXpMexYIW83Q4/2kqoGC1dyfbr6uGL946Pw69FcvLftDDKKa/D0mmP4j6czHhobgZlRQVA0BTt7V9eoRWqeCsdyK3HwbCmOZJZfshzIwBAP3BIZgGmRAQhQ2O8vWyJzEwQByXkqrD2Sg03JBahtmsNMKhYhpo8f5gwLwdgePnbZB06r0yMppxI7TxcZVyZvC2ubFPB62c93YkeCuxje6AqrGtCo1dt0/wyxWIQ5w0IxpX8AfojLwoqDmcgpr8Nrf57E25tP48bePrg1Ohg39PSGs8w+/jtqdXpkldXiWE4ljudW4lhOJdKKqqHTt1zY1t/dEWN6eGNsD2+M7u4NbysetklkiyrrGrHhWD7WJuTijLLauD3C2wV3DQ3B7EHB8HGzv5+7GrUW+9NLsON0Ef5Iym/z8/41rY/djqK1j3cXO+PjKoejgxgNGj0KKusR7u1i6ZKum8LZAU9P7IGHxkbg14Rc4y+f7SeLsP1kEWQSMQaHdcGYHt4Y090bvQPcrH4WZL1eQIGqHulF1UhT1jR9rsbZkppW1zXzc5cjOqQLhkZ44oYe3uju62qz97+JrFV9ow7xmWXYcCwfW04ojT+LcqkYUwcE4K6hIRge4Wl3P3tKVQN2ni7CztNF2NPOZYqylk0zUVXWg2HHColEIgR3ccbZ4hrkVtTZRdhp5iyTYt7oCMwbHYHThVXYcCwfm1MKkV9Zj7jzZYg7X4YPtqfBQSJCTz83DAhSoF+gO8K9XRDm6YIAD0ezdRjU6PQoq2lESbUa+ZX1yKuoQ0654SO3vA65FfWXXazVyUGC/kHuiA7tgugQDwwM9eCtKSIT0OkFnCxQYX9GKQ5klCIxu6LFuoK9/d1w97BQzBpoX7fNBUHAqcIq7DxVjO0nlThVeOXZjf/p/LtTO8XEiM0YdqxUSBcnQ9gpr7d0KSbTJ8AdfQLcsXhKb2SW1uLA2VLsSy9FQlY5VPUanCyowsmClj/AErEIgR6OCFA4oYuzAzxdZOjiLIOniwwucilkEjHkDuKmzxJIxSLo9AJ0egFavQCdXg+d3tCHpkatRU1D02e1FtUNWpTXGsJNSY36iovcNXOQiNDNxxU9/dzQy98NPf3c0NPPFSFdnDvVLxIic8otrzOEm7MlOHSu7JJpOgIVjhjf2xd3DQlBZLDCblpxGrV6xGeWYftJJX4+nNOu57rJpUh542a7uRbtxbBjpUI8nQEAOeV1Fq7E9EQiEbr6uKKrjyseGBkOQRCQV1GPE/kqpOarcEZZbWxNUWv1yC2vN1sIlIhF8HaVwd/dESGezght+mj+OkDh2OlHlhGZmqpOg0PnSrH/bCkOni1FdlnL34tucilGdPPC2Kbb4BHeLnbzpl5Z14idp4vx6a70dv/eW353NGZE2fccQW3FsGOlQroYwk5uhf2HnX8SiUQIaQoUUwYEGLfr9QJKatTILqtDSbUa5XWNqKhtRHnTR12jDmqtDo1aPdRaPRq1emj1ekjEYkjFIojFIkjFIkhEIjjJJHB1lMJNLoWrXApXR8NnTxcZfNzkhg9XObo4y9hCQ2Rmaq0OSdmVOHC2BAfOliE1rxIX9++XikWIDvXAmO4+GNPDG1HBCrv4o0MQBORX1iMxuwI/xWW3aU2qfzrz1mQ4Olh3f0dLYNixUhFN/XTOFtVYuBLrIRaL4OfuCL9OsNIwUWciCALSi2qwP6MEB86WIv58Oeo1uhbHdPd1xZjuhtGLw7t62cWw6Bq1Fil5lUjMqsCnuzKg/ceIzbb4/fGRXB+vDWz/f4udGhBsWGwuo7gadY1auxmWTUSk0emRpqxGar4KRzLLceBsKUqq1S2O8XaVY0x3L4zu7o0xPbxtvoO/Ti8go7gax3MqEZ9ZjvXH2j4k/GKv3dIXD46J6ODq7B/fQa2Un7sjfN3kKK5W41RBFYaEM7kTke3R6QWcK6lBSp4KKXmVSMlT4VRh1SUjGR0dxBgW4YWxTeGmt7+bTfe7Ka5uwPGcShzLrcSPh7KMExm211f3Dcbk/v4dXF3nw7BjxSKDPbDzdBFS8lQMO0Rk9QRBQHZZHZLzKpGap0JKngonClSoa+WN3t1RishgD0SFKDC6uzcGh3Wx+rm1LqdBo8OJfBWO5VRibUIOzpXUXvO5Di2egEA7Xq7CUhh2rFhksAI7TxchNV9l6VKIiFoQBAEFqgak5FYiJV/VFG4qUdWgveRYZ5kE/QMViAxWYECwAlHBHgjzcrbJlhtBEJBZWosjmeVYeSirxczM7dU3wB2xT4+xyetgaxh2rFhzv52UvErLFkJEnV5xdQNS81RIzlMhtel2VFkrc1HJpGL0DXBHZLACkcEeiAxWoJuPq02uO9Wg0eF8SS0Sssrx+saT130+jpSyHIYdKxYZZAg750pqUVzVAF+OQiIiE9PrBeRW1CGjqAZnlFVNfW1UULayMLFUbJjpPCpEgQFBhmDT08/N5tbza9TqkVlai7SiamxKLsCOU0XXfc4jL0/k72wrwrBjxbxc5YgKViA5T4XdZ4oxZ1iopUsiIjvRHGrSi2qQUVyNjCLD+m7nSmrQoLl0GRSRCOju42psrYkMVqBPgLtNtVRodHpkl9UivagGR7Mq8P3BzA457+l/T4aTzHauQ2fEsGPlYvr4ITlPhR2nihh2iKjddHoBeU2hJr2oGmeLrxxqAMOtqG4+rujh62roZxOkQP8gBVxsZG4brU6P7PI6ZBRV41hOJf6373yHnLennyu2L7qBfWxskG38z+3Eburnhw93pOPA2VLOt0NEl6XTC8gtr0NGU5jJKKpGRnENzhbXQH2ZBWubQ01PP0Ow6eHnhh6+rgj1dLaJGYmbv+czymrsOFWE35PyOuzcCa/EwMdN3mHnI8viO6eV6+XnhuAuTsirqMeBjFLc3I/zLRB1Zs1v8OlNYSajqBrpRTU4V3LlUNPdxxU9/AyL1nb3NXwO9XS2iY7DjVo98irqcDy3Es/9mtyh5+YMxJ0Dw46VE4lEiOnjh5WHsrAppZBhh6gT0Oj0yK+oR1ZZLbLL6pBZWovspq9zK+qg0bW+rID84paaplaaHjYSauobdcgpr0NGcTV+PJSNI1nlHXr+zQvHoH/ToA/qfBh2bMDtg4Ox8lAWtqQWYsmU3pxwisgOqLU65JbXI7usFllldS0+51XUQ3eFdZLkUjG6+7a89dTTzw0hVh5qqho0yGkKbz/FdXygAdhZmFrHsGMD+gcpMKqbFw6dK8OKg5l4ZVpfS5dERG3QoNEhu6yuqYXmolBTWocCVT2EK6z76OggRriXC8K8nJs+uyDcyxlh3i7wd3e0ylAjCALKaxuRVVaHs8XV+L/fU03yOq9M7YOHb+hqknOTfWLYsREP39AVh86VYc2RXCyc2APujg6WLomo02t+c8+vrEdeRT2yjS00hltOhapL56a5mItMYggx3s4I83JBRHO48XaBr5vcKkf96PUCiqvVOF9Sg7/TivHN/o4Zvv1PMqkYaW9NtsprQLaHYcdGjO/pgx6+rsgorsHPh7PxxPjuli6JyO7p9QJKatTIq6hvCjR1yK+oNz7Or6hHvebKCzy6OUoR4X1Ry8xFn71dZVb3Zt4c4PIq6nE0uwJvbT5lstcK9XTG3hfHW901IPvDsGMjRCIRHh3XDS+sS8Z/d5/FLQMCEerlbOmyiGyaVqdHUbUaeeV1xtaZ/IuCTUFlAxp1rY9wupivmxxBXZwQ5tnUQuN94faTh7ODVb2Za3V6KKsakN8UZj7YnmbS1/vi3kGYOiDApK9BdDUMOzbktuggrDuai/jMcrz4WzLWPDwCYiu8b09kLRo0OihVDcZWmLx/tM4oqxqu2BEYAMQiIEDhhCAPJwR3cUJQl6bPHs4I6uKEAIWjVc0iXNeoRUFlPXLL6/HN/vM4dK7M5K957t2pVtmHiKgZw44NEYtF+OD2KEz+dB/iM8vxQ1wW5o+OsHRZRBZRo9ZCqapHoaoBhaoGKFUNUFYZPhse16OiTnPV8zhIRAj0uCjMNIUYw9dO8Fc4wsFKJtgTBAEVdRrkVdThaFYF/m3CW0wXO/nmJJuZPZmoNfzfa2NCvZyxZGofvLrhBN7bdgYDghQYEs4Jsch+CIKAyjoNClUNKKq6EFwKm8JMoaoBRaoGVKu1bTqfo4MYQR5OCOribAw0wRe1zvi4ya2iVaK5r0yhqgHJeZV4Zf0Js712xjtTrCbQEZkCw44ZNWr1HbIa8L3DQrH7dBH+TivB3O+PYOWDwzCUgYdsQINGh+IqNYqrG1BcrUZxVQOKqtVNrTH1xlaZy80E/E9ujlIEKBzhr3BCgLsj/BUXPgIUjghwd4K7k9TifWYatXoUVxtanfaml+Cz3WfN9tr3Dg/FO7cOMNvrEVkjhh0zWnkoE4/c0O26zyMWi/DFvYPx0I8JOHi2DPMYeMiCBEFAtVprDDEl1ep/BJoLX1c3tK01BgC8XGTwc3dsCjOOF0KNwhF+TcHG1QpurVQ3aFBU1YCzxTV47Ocks7/+2Xem2MQ6VkSWJBKEK01r1TlUVVVBoVBApVLB3d29Q88dvji2xeOsZdM67Nz1jTpj4HFykODlaX1w77BQdlqmDqHV6VFe14jS6kaU1BhaYYqr1YYwU93QFGIMX19u9ezWyKVi+LrL4evmCF83uTG4BCgc4e/uiACFE3zd5Rbv9Nug0aGkWo3c8jo8+lNim2+bdSTeXiK6sra+fzPswLRhJzm3EjM/P2h83JFhBzAEnkd/TsS+9BIAwMiuXnj/9kiEeHJYOl2q+Q28rLYRpdVqlNWqUVrT2Oq2irrGK87w+09ucil83OXwdbsQZC4ONb7ucvi4OcLd0XK3lS5uhcouq8WCH45apA5vVxkSXomx+O01IlvX1vdvy7cB27l+gR0bnv7JSSbBynlD8UNcFt7floa482WY9Mk+PDG+G+4dHoYuLjKTvj5ZlkanR0VdIypqNSivbUR5baMxrJTWqJvCi+HrsppG1LSzdUIsAjxdZPB2lcOnOcRcHGgu+tqS6xHp9QLKahtRVNWAg2dLsXTrGYvVcmjxBK5fR2RlGHZMzBz30sViEeaPjsCE3r546bcUxGeW4z9/peOz3Wdxa3QQ5o0OR29/04Yuun6CIKCqQYuK2kaU1zWivMbwuaIpxJTXGlpbymovbKtqRx+YZjKJGN6uMni7yeHtKoeXi+FrLxcZfNzk8HKRw9vNEHC6OMssNlKp+XqU1qhxprAaT642f3+Yi616aDhGd/e2aA1EdG0YduxImJcL1jw8An8m5+O7A5k4kV+FtQm5WJuQi8FhXXBjLx+M7eGDAUEK9usxIUEQUNuoQ2VdIyrrNFDVa1BZp0Fl/cWPG5u2aaCq0xhDjfYqE9y1RiQCujjL0MXZAZ4uMmNYMXyWw8dVBi/XpmDjKoOb3HK3kfR6AZX1GpTWqHGqoAqLfjlukToudnDxBASxJYbIrjHs2BmxWIRbo4Mxa2AQjmZXYOXBLGw7qURidgUSsyvwn7/S0cXZAaO7e2NEVy/08ndDT183KJy5sOjFNDo9qhu0qKrXGD43aFDdoEFVveHrqqZ9VQ2GsFLZFGCag821hJZmLjIJurjI4Nn84Sxr8biLswxerobPni4yKJwcLDpPTHNH5iKVGm9tPoUjWeUWq6WZv7sj4pZMYJ8YIgLAsGO3RCIRhoZ7Ymi4JwpV9dh1uhj70ktw6FwZKuo02JxSiM0phcbjfd3k6OXvhh6+bgj1dIKvu2NTHw1DXw1nmfX/V9Hq9Kht1KFWrUVdoxY1asPXtWotapse1xkfG/bVNH0YgovWGGiutrhjW8gkYng4Oxg+nGRQODvAw6npsbMhpHg4O0Dh5NAiyFh6FJJaqzP0/alpRGxqIb7cc86i9VyMw6yJ6FpY/zsYXbcAhRPuGxGG+0aEQaPT43huJfallyAlT4WMomoUqJrmQ6lWY39GaavncJVL4eMmh5ujFE4OEjjLJHCWS+Hc9LWTTApnmQQSsQgSsQhiESAWiZo+DC1OzY91ggCdTg+tXoBWL0CnF6DR6aH7x2ONTo8GjR4NGh0aNHqotTrj1w0aHRq0F75Wa/RtWrCxvVxkErg5OsDdSWr47Cj9x+PmMOPQFGZk8HB2aAotYqtoWahr1KKsxtB597lfk5FTXmfpklrIXDrVKq4TEdkvhp1OxkEiNrb4NKtu0CCjuAYZRdVIL6pBQWU9SqrVTXOrqFGv0RlbQGyBg0QEF7kULjIpXOSSS752lUvhLJPCVS6Bs0wKN0cp3J0cDJ+bAoy7k+E4a2tFaB46XVbTiBP5Kixcc8zSJV3iwzuiMHtwsKXLICIyYtghuDk6YFBoFwwK7XLJvubOtsVVhplxaxu1qFXrUN+oQ12j4XaQ4Wsd6jVaaHUC9ILheXrB8LVOEAyP9YBeEIytP1KxCFKJGNLLPZaI4egghqNUAkcHieFrBwmcHCSQN31t2Nf0tYMELnIJ5FLrWYH6ajQ6fdM6UPW49YtDV12B2xJu7OWDFfOHWboMIqJrxrBjZjq9YBWLDraVSCSCq1wKVx9XdPVxtXQ5Vq1Bo0NFXSOKqtR4+MejKKlWW7qkVn1weyTuGBJi6TKIiMyGYcfMur28pcNnUaaO1dyaVV7TiJT8Sjy12vpuFV2MfV6IiK6MYccMfnlkBO76+rCly+iU1FodVHUaFKga8ODKBJTXNlq6pCv69dGRGBbBBV2JiDoSw44Z8M3r+giCgAaNHpX1huHQ7207c9lRY9bk6/sH4+Z+/pYug4io02PYMYN/3mKwtX47HUUQBNQ16lBZr0F+RT3u/F+cpUtqM64+TURkuxh2LMCW++3o9AJqmmYULq9txKr4bPx6NM/SZbUZW1uIiDofkSAI1jfW9Rp8/vnn+OCDD6BUKhEVFYXPPvsMw4a1bbhsW5eIvx7nSmow8cO9LbZZIvA0avXGmYNV9Rrc/fVhVNvI/DkX+7/JvfH4+G6WLoOIiCyore/fdtGy88svv+C5557DV199heHDh+OTTz7BpEmTkJaWBl9fX0uXBwDo1sqw7fDFsRaoxLoc/VcMvF3lli6DiIjsmF207AwfPhxDhw7Ff//7XwCAXq9HSEgIFi5ciMWLF1/1+eZo2WlmjwHntuggfHTXQEuXQUREnUynadlpbGxEYmIilixZYtwmFosRExODuLjWO8Cq1Wqo1RcmfKuqqjJ5nc2ylk3D/d/FW9VoovdnR+LOoZxkjoiI7JPNh53S0lLodDr4+fm12O7n54czZ860+pylS5fizTffNEd5rfppwXCLvTYREVFn0ynH0i5ZsgQqlcr4kZuba+mSiIiIyERsvmXH29sbEokERUVFLbYXFRXB37/1IcZyuRxyOTvFEhERdQY237Ijk8kwePBg7Nq1y7hNr9dj165dGDlypAUrIyIiImtg8y07APDcc89h7ty5GDJkCIYNG4ZPPvkEtbW1mD9/vqVLIyIiIguzi7Bz1113oaSkBK+99hqUSiUGDhyIbdu2XdJpmYiIiDofu5hn53qZc54dIiIi6hhtff+2+T47RERERFfCsENERER2jWGHiIiI7BrDDhEREdk1hh0iIiKyaww7REREZNcYdoiIiMiuMewQERGRXbOLGZSvV/O8ilVVVRauhIiIiNqq+X37avMjM+wAqK6uBgCEhIRYuBIiIiJqr+rqaigUisvu53IRMKySXlBQADc3N4hEog45Z1VVFUJCQpCbm8slKEyI19k8eJ3Ng9fZPHidzcMc11kQBFRXVyMwMBBi8eV75rBlB4BYLEZwcLBJzu3u7s4fJjPgdTYPXmfz4HU2D15n8zD1db5Si04zdlAmIiIiu8awQ0RERHaNYcdE5HI5Xn/9dcjlckuXYtd4nc2D19k8eJ3Ng9fZPKzpOrODMhEREdk1tuwQERGRXWPYISIiIrvGsENERER2jWGHiIiI7BrDjol8/vnnCA8Ph6OjI4YPH44jR45YuiSbtXTpUgwdOhRubm7w9fXFrFmzkJaW1uKYhoYGPPnkk/Dy8oKrqytmz56NoqIiC1VsH5YtWwaRSIRFixYZt/E6d4z8/Hzcd9998PLygpOTEwYMGICjR48a9wuCgNdeew0BAQFwcnJCTEwMMjIyLFix7dHpdHj11VcREREBJycndOvWDW+99VaLNZR4ndtv3759mD59OgIDAyESibBhw4YW+9tyTcvLy3HvvffC3d0dHh4eWLBgAWpqakxbuEAdbu3atYJMJhO+//574eTJk8LDDz8seHh4CEVFRZYuzSZNmjRJWLFihXDixAnh+PHjwtSpU4XQ0FChpqbGeMxjjz0mhISECLt27RKOHj0qjBgxQhg1apQFq7ZtR44cEcLDw4XIyEjhmWeeMW7ndb5+5eXlQlhYmDBv3jwhPj5eOH/+vLB9+3bh7NmzxmOWLVsmKBQKYcOGDUJycrIwY8YMISIiQqivr7dg5bblnXfeEby8vITNmzcLmZmZwrp16wRXV1fh008/NR7D69x+W7ZsEV555RXhjz/+EAAI69evb7G/Ldd08uTJQlRUlHD48GFh//79Qvfu3YW7777bpHUz7JjAsGHDhCeffNL4WKfTCYGBgcLSpUstWJX9KC4uFgAIe/fuFQRBECorKwUHBwdh3bp1xmNOnz4tABDi4uIsVabNqq6uFnr06CHs2LFDGDdunDHs8Dp3jP/7v/8TxowZc9n9er1e8Pf3Fz744APjtsrKSkEulwtr1qwxR4l2Ydq0acKDDz7YYtttt90m3HvvvYIg8Dp3hH+GnbZc01OnTgkAhISEBOMxW7duFUQikZCfn2+yWnkbq4M1NjYiMTERMTExxm1isRgxMTGIi4uzYGX2Q6VSAQA8PT0BAImJidBoNC2uee/evREaGsprfg2efPJJTJs2rcX1BHidO8rGjRsxZMgQ3HHHHfD19UV0dDS++eYb4/7MzEwolcoW11mhUGD48OG8zu0watQo7Nq1C+np6QCA5ORkHDhwAFOmTAHA62wKbbmmcXFx8PDwwJAhQ4zHxMTEQCwWIz4+3mS1cSHQDlZaWgqdTgc/P78W2/38/HDmzBkLVWU/9Ho9Fi1ahNGjR6N///4AAKVSCZlMBg8PjxbH+vn5QalUWqBK27V27VokJSUhISHhkn28zh3j/Pnz+PLLL/Hcc8/h5ZdfRkJCAp5++mnIZDLMnTvXeC1b+x3C69x2ixcvRlVVFXr37g2JRAKdTod33nkH9957LwDwOptAW66pUqmEr69vi/1SqRSenp4mve4MO2RTnnzySZw4cQIHDhywdCl2Jzc3F8888wx27NgBR0dHS5djt/R6PYYMGYJ3330XABAdHY0TJ07gq6++wty5cy1cnf349ddfsWrVKqxevRr9+vXD8ePHsWjRIgQGBvI6d0K8jdXBvL29IZFILhmhUlRUBH9/fwtVZR+eeuopbN68GX///TeCg4ON2/39/dHY2IjKysoWx/Oat09iYiKKi4sxaNAgSKVSSKVS7N27F8uXL4dUKoWfnx+vcwcICAhA3759W2zr06cPcnJyAMB4Lfk75Pq8+OKLWLx4MebMmYMBAwbg/vvvx7PPPoulS5cC4HU2hbZcU39/fxQXF7fYr9VqUV5ebtLrzrDTwWQyGQYPHoxdu3YZt+n1euzatQsjR460YGW2SxAEPPXUU1i/fj12796NiIiIFvsHDx4MBweHFtc8LS0NOTk5vObtMHHiRKSmpuL48ePGjyFDhuDee+81fs3rfP1Gjx59ydQJ6enpCAsLAwBERETA39+/xXWuqqpCfHw8r3M71NXVQSxu+RYnkUig1+sB8DqbQluu6ciRI1FZWYnExETjMbt374Zer8fw4cNNV5zJuj53YmvXrhXkcrmwcuVK4dSpU8IjjzwieHh4CEql0tKl2aTHH39cUCgUwp49e4TCwkLjR11dnfGYxx57TAgNDRV2794tHD16VBg5cqQwcuRIC1ZtHy4ejSUIvM4d4ciRI4JUKhXeeecdISMjQ1i1apXg7Ows/Pzzz8Zjli1bJnh4eAh//vmnkJKSIsycOZNDottp7ty5QlBQkHHo+R9//CF4e3sLL730kvEYXuf2q66uFo4dOyYcO3ZMACB89NFHwrFjx4Ts7GxBENp2TSdPnixER0cL8fHxwoEDB4QePXpw6Lmt+uyzz4TQ0FBBJpMJw4YNEw4fPmzpkmwWgFY/VqxYYTymvr5eeOKJJ4QuXboIzs7Owq233ioUFhZarmg78c+ww+vcMTZt2iT0799fkMvlQu/evYWvv/66xX69Xi+8+uqrgp+fnyCXy4WJEycKaWlpFqrWNlVVVQnPPPOMEBoaKjg6Ogpdu3YVXnnlFUGtVhuP4XVuv7///rvV38dz584VBKFt17SsrEy4++67BVdXV8Hd3V2YP3++UF1dbdK6RYJw0XSSRERERHaGfXaIiIjIrjHsEBERkV1j2CEiIiK7xrBDREREdo1hh4iIiOwaww4RERHZNYYdIiIismsMO0RERGTXGHaIyG7dcMMNWL169RWP+eqrrzB9+nQzVURElsCwQ0R2aePGjSgqKsKcOXOM20QiETZs2NDiuAcffBBJSUnYv3+/mSskInNh2CEiu7R8+XLMnz//kpWv/0kmk+Gee+7B8uXLzVQZEZkbww4R2Zwff/wRXl5eUKvVLbbPmjUL999/P0pKSrB79+4Wt6fCw8MBALfeeitEIpHxMQBMnz4dGzduRH19vTnKJyIzY9ghIptzxx13QKfTYePGjcZtxcXFiI2NxYMPPogDBw7A2dkZffr0Me5PSEgAAKxYsQKFhYXGxwAwZMgQaLVaxMfHm++bICKzYdghIpvj5OSEe+65BytWrDBu+/nnnxEaGorx48cjOzsbfn5+LW5h+fj4AAA8PDzg7+9vfAwAzs7OUCgUyM7ONt83QURmw7BDRDbp4Ycfxl9//YX8/HwAwMqVKzFv3jyIRCLU19fD0dGxXedzcnJCXV2dKUolIguTWroAIqJrER0djaioKPz444+4+eabcfLkScTGxgIAvL29UVFR0a7zlZeXt2jtISL7wbBDRDbroYcewieffIL8/HzExMQgJCQEgCEIKZVKVFRUoEuXLsbjHRwcoNPpLjnPuXPn0NDQgOjoaLPVTkTmw9tYRGSz7rnnHuTl5eGbb77Bgw8+aNweHR0Nb29vHDx4sMXx4eHh2LVrlzEINdu/fz+6du2Kbt26ma12IjIfhh0islkKhQKzZ8+Gq6srZs2aZdwukUgwf/58rFq1qsXxH374IXbs2IGQkJAWrThr1qzBww8/bK6yicjMRIIgCJYugojoWk2cOBH9+vW7ZFJApVKJfv36ISkpCWFhYZd9/smTJzFhwgSkp6dDoVCYulwisgCGHSKySRUVFdizZw9uv/12nDp1Cr169brkmA0bNsDLywtjx4697Hl27twJnU6HSZMmmbJcIrIghh0isknh4eGoqKjAq6++ihdeeMHS5RCRFWPYISIiIrvGDspERERk1xh2iIiIyK4x7BAREZFdY9ghIiIiu8awQ0RERHaNYYeIiIjsGsMOERER2TWGHSIiIrJr/w/4Mu8g2skRsQAAAABJRU5ErkJggg=="
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 26
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "#### Time delay Chen system\n",
    "\n",
    "Time delay Chen system as a famous chaotic system with time delay, has important applications in many fields.\n",
    "\n",
    "$$\n",
    "\\left\\{\\begin{array}{l}\n",
    "D^{\\alpha_{1}} x=a(y(t)-x(t-\\tau)) \\\\\n",
    "D^{\\alpha_{2}} y=(c-a) x(t-\\tau)-x(t) z(t)+c y(t) \\\\\n",
    "D^{\\alpha_{3}} z=x(t) y(t)-b z(t-\\tau)\n",
    "\\end{array}\\right.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2025-10-06T04:05:31.479406Z",
     "start_time": "2025-10-06T04:05:31.040732Z"
    }
   },
   "source": [
    "dt = 0.001\n",
    "tau = 0.009\n",
    "xdelay = bm.TimeDelay(bm.asarray([0.2]), tau, dt=dt)\n",
    "zdelay = bm.TimeDelay(bm.asarray([0.5]), tau, dt=dt)\n",
    "\n",
    "\n",
    "def derivative(x, y, z, t):\n",
    "    a = 35;\n",
    "    b = 3;\n",
    "    c = 27\n",
    "    dx = a * (y - xdelay(t - tau))\n",
    "    dy = (c - a) * xdelay(t - tau) - x * z + c * y\n",
    "    dz = x * y - b * zdelay(t - tau)\n",
    "    return dx, dy, dz\n",
    "\n",
    "\n",
    "integral = bp.fde.GLShortMemory(derivative,\n",
    "                                alpha=0.94,\n",
    "                                inits=[0.2, 0., 0.5],\n",
    "                                num_memory=500,\n",
    "                                state_delays={'x': xdelay, 'z': zdelay})"
   ],
   "outputs": [],
   "execution_count": 27
  },
  {
   "cell_type": "code",
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2025-10-06T04:05:49.521536Z",
     "start_time": "2025-10-06T04:05:31.490008Z"
    }
   },
   "source": [
    "runner = bp.IntegratorRunner(integral,\n",
    "                             inits=[0.2, 0., 0.5],\n",
    "                             monitors=['x', 'y', 'z'],\n",
    "                             dyn_vars=xdelay.vars() + zdelay.vars(),\n",
    "                             dt=dt)\n",
    "runner.run(100.)"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "  0%|          | 0/100000 [00:00<?, ?it/s]"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "ce63afe9fd40433fa2d58cdcb489a141"
      }
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 28
  },
  {
   "cell_type": "code",
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2025-10-06T04:05:52.039259Z",
     "start_time": "2025-10-06T04:05:51.923327Z"
    }
   },
   "source": [
    "fig = plt.figure()\n",
    "ax = plt.axes(projection='3d')\n",
    "plt.plot(runner.mon.x[:, 0], runner.mon.y[:, 0], runner.mon.z[:, 0])\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 29
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "#### Enzyme kinetics\n",
    "\n",
    "Let's see a more complex example of the fractional order version of enzyme kinetics with an inhibitor molecule:\n",
    "\n",
    "$$\n",
    "\\begin{gathered}\n",
    "D_{t}^{\\alpha} y_{1}(t)=10.5-\\frac{y_{1}(t)}{1+0.0005 y_{4}^{3}(t-4)} \\\\\n",
    "D_{t}^{\\alpha} y_{2}(t)=\\frac{y_{1}(t)}{1+0.0005 y_{4}^{3}(t-4)}-y_{2}(t) \\\\\n",
    "D_{t}^{\\alpha} y_{3}(t)=y_{2}(t)-y_{3}(t) \\\\\n",
    "D_{t}^{\\alpha} y_{4}(t)=y_{3}(t)-0.5 y_{4}(t) \\\\\n",
    "y(t)=[60,10,10,20], t \\leq 0\n",
    "\\end{gathered}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2025-10-06T04:05:52.508168Z",
     "start_time": "2025-10-06T04:05:52.043738Z"
    }
   },
   "source": [
    "dt = 0.01\n",
    "tau = 4.\n",
    "delay = bm.TimeDelay(bm.asarray([20.]), tau, before_t0=20, dt=dt)\n",
    "\n",
    "\n",
    "def derivative(a, b, c, d, t):\n",
    "    da = 10.5 - a / (1 + 0.0005 * delay(t - tau) ** 3)\n",
    "    db = a / (1 + 0.0005 * delay(t - tau) ** 3) - b\n",
    "    dc = b - c\n",
    "    dd = c - 0.5 * d\n",
    "    return da, db, dc, dd\n",
    "\n",
    "\n",
    "integral = bp.fde.GLShortMemory(derivative,\n",
    "                                alpha=0.95,\n",
    "                                inits=[60, 10, 10, 20],\n",
    "                                num_memory=500,\n",
    "                                state_delays={'d': delay})"
   ],
   "outputs": [],
   "execution_count": 30
  },
  {
   "cell_type": "code",
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2025-10-06T04:05:54.303410Z",
     "start_time": "2025-10-06T04:05:52.514195Z"
    }
   },
   "source": [
    "runner = bp.IntegratorRunner(integral,\n",
    "                             inits=[60, 10, 10, 20],\n",
    "                             monitors=list('abcd'),\n",
    "                             dyn_vars=delay.vars(),\n",
    "                             dt=dt)\n",
    "runner.run(200.)"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "  0%|          | 0/20000 [00:00<?, ?it/s]"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "713348e50a2e4e47a37975b23c8e5491"
      }
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 31
  },
  {
   "cell_type": "code",
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2025-10-06T04:05:54.620047Z",
     "start_time": "2025-10-06T04:05:54.346378Z"
    }
   },
   "source": [
    "plt.plot(runner.mon.ts, runner.mon.a, label='a')\n",
    "plt.plot(runner.mon.ts, runner.mon.b, label='b')\n",
    "plt.plot(runner.mon.ts, runner.mon.c, label='c')\n",
    "plt.plot(runner.mon.ts, runner.mon.d, label='d')\n",
    "plt.legend()\n",
    "plt.xlabel('Time [ms]')\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 32
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "#### Fractional matrix delayed differential equations\n",
    "\n",
    "BrainPy is also capable of solving fractional matrix delayed differential equations:\n",
    "\n",
    "$$\n",
    "D_{t_{0}}^{\\alpha} \\mathbf{x}(t)=\\mathbf{A}(t) \\mathbf{x}(t)+\\mathbf{B}(t) \\mathbf{x}(t-\\tau)+\\mathbf{c}(t)\n",
    "$$\n",
    "\n",
    "Here $x(t)$ is vector of states of the system, $c(t)$ is a known function of disturbance.\n",
    "\n",
    "We explain the detailed usage by using an example:\n",
    "\n",
    "$$\n",
    "\\mathbf{x}(t)=\\left(\\begin{array}{l}\n",
    "x_{1}(t) \\\\\n",
    "x_{2}(t) \\\\\n",
    "x_{3}(t) \\\\\n",
    "x_{4}(t)\n",
    "\\end{array}\\right)\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\mathbf{A}=\\left(\\begin{array}{cccc}\n",
    "0 & 0 & 1 & 0 \\\\\n",
    "0 & 0 & 0 & 1 \\\\\n",
    "0 & -2 & 0 & 0 \\\\\n",
    "-2 & 0 & 0 & 0\n",
    "\\end{array}\\right)\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\mathbf{B}=\\left(\\begin{array}{cccc}\n",
    "0 & 0 & 0 & 0 \\\\\n",
    "0 & 0 & 0 & 0 \\\\\n",
    "-2 & 0 & 0 & 0 \\\\\n",
    "0 & -2 & 0 & 0\n",
    "\\end{array}\\right)\n",
    "$$\n",
    "\n",
    "With initial condition:\n",
    "\n",
    "$$\n",
    "\\mathbf{x}_{0}(t)=\\left(\\begin{array}{c}\n",
    "\\sin (t) \\cos (t) \\\\\n",
    "\\sin (t) \\cos (t) \\\\\n",
    "\\cos ^{2}(t)-\\sin ^{2}(t) \\\\\n",
    "\\cos ^{2}(t)-\\sin ^{2}(t)\n",
    "\\end{array}\\right)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2025-10-06T04:05:54.862383Z",
     "start_time": "2025-10-06T04:05:54.626322Z"
    }
   },
   "source": [
    "dt = 0.01\n",
    "tau = 3.1416\n",
    "f = lambda t: bm.asarray([bm.sin(t) * bm.cos(t),\n",
    "                          bm.sin(t) * bm.cos(t),\n",
    "                          bm.cos(t) ** 2 - bm.sin(t) ** 2,\n",
    "                          bm.cos(t) ** 2 - bm.sin(t) ** 2])\n",
    "delay = bm.TimeDelay(f(0.), tau, before_t0=f, dt=dt)\n",
    "\n",
    "A = bm.asarray([[0, 0, 1, 0], [0, 0, 0, 1], [0, -2, 0, 0], [-2, 0, 0, 0]])\n",
    "B = bm.asarray([[0, 0, 0, 0], [0, 0, 0, 0], [-2, 0, 0, 0], [0, -2, 0, 0]])\n",
    "c = bm.asarray([0, 0, 0, 0])\n",
    "derivative = lambda x, t: A @ x + B @ delay(t - tau) + c\n",
    "\n",
    "integral = bp.fde.GLShortMemory(derivative,\n",
    "                                alpha=0.4,\n",
    "                                inits=[f(0.)],\n",
    "                                num_memory=500,\n",
    "                                state_delays={'x': delay})"
   ],
   "outputs": [],
   "execution_count": 33
  },
  {
   "cell_type": "code",
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2025-10-06T04:05:55.404420Z",
     "start_time": "2025-10-06T04:05:54.867798Z"
    }
   },
   "source": [
    "runner = bp.IntegratorRunner(integral,\n",
    "                             inits=[f(0.)],\n",
    "                             monitors=['x'],\n",
    "                             dyn_vars=delay.vars(),\n",
    "                             dt=dt)\n",
    "runner.run(100.)"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "  0%|          | 0/10000 [00:00<?, ?it/s]"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "60d33504d48a4ebf9dbe9b3a226ce292"
      }
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 34
  },
  {
   "cell_type": "code",
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2025-10-06T04:05:55.476599Z",
     "start_time": "2025-10-06T04:05:55.409856Z"
    }
   },
   "source": [
    "plt.plot(runner.mon.x[:, 0], runner.mon.x[:, 2])\n",
    "plt.xlabel('x0')\n",
    "plt.ylabel('x2')\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
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     "metadata": {},
     "output_type": "display_data",
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   ],
   "execution_count": 35
  },
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   "source": [
    "## Acknowledgement"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This tutorial is highly inspired from the work of Ettore Messina [1] and of Qingyu Qu [2].\n",
    "\n",
    "- [1] Computational Mindset by Ettore Messina, [Solving delay differential equations using numerical methods in Python](https://computationalmindset.com/en/mathematics/solving-delay-differential-equations-in-python-using-numerical-methods.html)\n",
    "- [2] [Fractional Order Delayed Differential Equations](https://scifracx.org/FractionalDiffEq.jl/dev/fdde/)"
   ]
  }
 ],
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